PHY2049L_book.pdf

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Florida International University

GENERAL PHYSICS

LABORATORY 2

MANUAL Edited Fall 2019

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Florida International University

Department of Physics

Physics Laboratory Manual for Course

PHY 2049L

Contents

Course Syllabus 2

Grading Rubric 4

Estimation of Uncertainties 5

Vernier Caliper 9

Experiments

1. Electrostatics 10

2. Coulomb's Law 13

3. Electric Field and Potential 16

4. Capacitors 21

5. Ohm's Law and Resistance 27

6. Series and Parallel Circuits 33

7. Magnetic Force on Moving Charges 40

8. Magnetic Field of a Solenoid 44

9. Faraday's Law & Lenz's Law 49

10. Reflection & Refraction 53

11. Mirrors, Lenses, Telescope 57

12. Double-Slit Interference 62

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COURSE SYLLABUS

LAB COORDINATOR

Email: Please use Canvas Inbox

UPDATES

Updates to the lab schedule, make-up policy, etc. may be found on Canvas.

CLASS MEETINGS

• During Fall and Spring Semesters classes start the second week of the semester and end the week prior to the final exam week.

• Students that have missed their own section may attempt to make-up by attending another section during the time the same experiment is conducted (see PantherSoft for

available sections). Admission for make-up is granted by the Instructor on site, no

reservation, no guaranteed seating.

• Students must sign in each class meeting to verify attendance.

ACTIVE LEARNING

One of the important goals of this lab course is to strengthen your understanding of what you

have learned in the classroom. You will be working in groups and encouraged to help each other

by discussing among yourselves any difficulties or misconceptions that occur to you. Apart from

the instructor in charge, student Learning Assistants (LA) will be on hand to encourage

discussion, for example by posing a series of questions.

LAB REPORTS

You will be required to submit a lab report at the end of the class period. The format of the report

is dictated by the experiment. As you work your way through the experiment, following the

procedures in this manual, you will be asked to answer questions, fill in tables of data, sketch

graphs, do straightforward calculations, etc. You should fulfill each of these requirements as you

proceed with the experiment. Any preliminary questions could be answered before coming to the

lab, thereby saving time. This way, you will effectively finish the report as you finish the

experiment. Note that for experiments that require them, blank or partially filled in data tables

are provided on separate perforated pages in this manual at the end of the experiment. You may

carefully tear them out along the perforation and staple them to the rest of your report.

GRADES

• The weekly lab reports and your active participation will determine your grade in the

course. Each week you will receive 30% for active participation and up to 70% for your lab

report.

• A missed assignment or lab will receive a ZERO grade.

• Lab reports are to be handed in before you leave the lab.

• THERE IS NO FINAL EXAM

• The grading system is based on the following scale although your instructor may apply a

"curve" if it is deemed necessary. In addition, “+” and “-“may be assigned in each grade

range when appropriate.

o A: 90-100%

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o B: 75-90% o C: 60-75% o D: 45-60%

WHAT YOU NEED TO PROVIDE

Calculator with trig. and other math functions including mean and standard deviation.

AT THE END OF CLASS.

1. Disconnect all sensors that you have connected. 2. Report any broken or malfunctioning equipment. 3. Arrange equipment tidily on the bench.

DROPPING THE LECTURE BUT NOT THE LAB

If you find it necessary to drop the lecture course, PHY 2049 or PHY 2054, you do not also have

to drop this lab course, PHY 2049L. However, you will need to see a Physics Advisor and get a

waiver.

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GRADING RUBRIC

Expectations for a successfully completed experiment and lab report are indicated in the

following rubric. Note that not every scientific ability in the rubric may be tested in every

experiment. Therefore, the graders will determine the maximum number of points attainable for

an experiment (usually 18) and indicate your score as a fraction, e.g 16/18.

Grade Scientific

ability

Missing

(0 pt)

Inadequate

(1 pt)

Needs

improvement

(2 pt)

Adequate

(3 pt)

Attempt to

answer

Preliminary

Questions

No attempt to

answer

Preliminary

Questions

Answers to

Preliminary

Questions

attempted

Able to draw

graphs/diagrams

No graphs or

drawings

provided

Graphs/drawings

poorly drawn with

missing axis labels

or important

information is

wrong or missing

Graphs/drawings

have no wrong

information but a

small amount of

information is

missing

Graphs/drawings

contain no

omissions and are

clearly presented

Able to present

data and tables

No data or

tables

provided

Not all the relevant

data and tables are

provided

Data and tables are

provided but some

information such as

units is missing

Complete set of

data and tables

with all necessary

information

provided

Able to analyze

data

No data

analysis or

analysis

contains

numerous

errors

Data analysis

contains a number

of errors indicating

substantial lack of

understanding

Data analysis is

mostly correct but

some lack of

understanding is

present

Data analysis is

complete with no

errors

Able to answer

Analysis

questions

No Analysis

questions

answered

Less than half the

questions

unanswered or

answered

incorrectly

Less than a quarter

of the questions

unanswered or

answered

incorrectly

All questions

answered

correctly

Able to conduct

experiment as

evidenced by the

quality of results

Little or no

experimental

ability as

evidenced by

poor quality of

results

Results indicate a

marginal level of

experimental ability

Results indicate a

reasonable level of

experimental

ability with room

for improvement

Results indicate a

proficient level of

experimental

ability

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ESTIMATION OF UNCERTAINTIES

The purpose of this section is to provide you with the rules for determining the uncertainties in

your experimental results. All measurements have some uncertainty in the results due to the fact

you can never do a perfect experiment. We begin with the rules for estimating uncertainties in

individual measurements, and then show how these uncertainties are to be combined to produce

the uncertainty in the final result.

The “absolute uncertainty” in a measured quantity is expressed in the same units as the quantity

itself. For example, length of table = 1.65 ± 0.05 m or, symbolically, L ± L. This means we are

reasonably confident that the length of the table is between 1.60 and 1.70 m, and 1.65 m is our

best estimate. If L is based on a single measurement, it is often a good rule of thumb to make L

equal to half the smallest division on the measuring scale. In the case of a meter rule, this would

be 0.5 mm. Other considerations, such as a rounded edge to the table, may make us wish to

increase L. For example, in the diagram, the end of the table might be estimated to be to be at

35.3 ± 0.1 cm or even 35.3 ± 0.2 cm.

If the same measurement is repeated several times, the average (mean) value is taken as the most

probable value and the “standard deviation” is used as the absolute uncertainty. Therefore, if the

length of the table is measured 3 times giving values of 1.65, 1.60 and 1.85m, the average value

is

The deviations of the 3 values from the average are -0.05, -0.10 and +0.15m, and the standard

deviation

So now we express the length of the table as 1.7 ± 0.1 m.

Note: Your calculator should be capable of providing the mean and standard deviation

automatically. Excel can also be used to calculate these quantities.

165 160 185

3 170

   

+ + = m

= sum of squares of deviations

number of measurements

= + +

= 0 05 010 015

3 01

2 2 2. . . . m

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Generally, it is only necessary to quote an uncertainty to one, or at most two, significant

figures, and the accompanying measurement is rounded off (not truncated) in the same decimal

position.

“Fractional uncertainty” or “percentage uncertainty” is the absolute uncertainty, expressed as a

fraction or percentage of the associated measurement. In the above example, the fractional

uncertainty, L/L is 0.1/1.7 = 0.06, and the percentage uncertainty is 0.06 x 100 = 6%.

Rules for obtaining the uncertainty in a calculated result.

We now need to consider how uncertainties in measured quantities are to be combined to

produce the uncertainty in the final result. There are 2 basic rules:

A) When quantities are added or subtracted, the absolute uncertainty in the result is equal to

the square root of the sum of the squares of the absolute uncertainties in the quantities.

B) When quantities are multiplied or divided, the fractional uncertainty in the result is equal

to the square root of the sum of the squares of the fractional uncertainties in the

quantities.

Examples

1. In calculating a quantity x using the formula x = a + b - c, measurements give

a = 2.1 ± 0.2 kg

b = 1.6 ± 0.1 kg

c = 0.8 ± 0.1 kg

Therefore, x = 2.9 kg

The result is therefore x = 2.9 ± 0.2 kg

2. In calculating a quantity x using the formula x = ab/c, measurements give

a = 0.75 ± 0.01 kg

b = 0.81 ± 0.01 m

c = 0.08 ± 0.02 m

Therefore x = 7.59375 kg (by calculator).

Fractional uncertainty in x,

x

x =

0.01

0.75

 

 

2

+ 0.01

0.81

 

 

2

+ 0.02

0.08

 

 

2

= 0.25

Absolute uncertainty in x, x = 0.25  7.59375

= 2 kg (to one significant figure)

The result is therefore x = 8 ± 2 kg

Note: the value of x has to be rounded in accordance with the value of x. If x had been

calculated to be 0.003 kg, the result would have been x = 7.594 ± 0.003 kg.

3. The following example involves both rule A and rule B.

In calculating a quantity x using the formula x = (a + b)/c, measurements give

Absoluteerror in x x kg, . . . . = + + =0 2 01 01 0 22 2 2

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a = 0.42 ± 0.01 kg

b = 1.63 ± 0.02 kg

c = 0.0043 ± 0.0004 m3

Therefore x = 476.7 kg/m3

Absolute uncertainty in kg 02.002.001.0 22 =+=+ ba

Fractional uncertainty in a + b = 0.02 / 2.05 = 0.01

Fractional uncertainty in c = 0.0004 / 0.0043 = 0.093

Fractional uncertainty in 094.001.0093.0 22 =+=x

Absolute uncertainty in x, x = 0.094 476.7 = 40 kg/m3 (to one significant figure)

The result is therefore x = 480 ± 40 kg/m3

Note that almost all of the uncertainty here is due to the uncertainty in c. One should therefore

concentrate on improving the accuracy with which c is measured in attempting to decrease the

uncertainty.

Uncertainty in the slope of a graph

Often, one of the quantities used in calculating a final result will be the slope of a graph.

Therefore, we need a rule for determining the uncertainty in the slope. Graphing software such as

Excel can do this for you. Another way to do this is “by hand” as follows: In drawing the best

straight line (see figure on following page),

1. The deviations of the data points from the line should be kept to a minimum. 2. The points should be as evenly distributed as possible on either side of the line. 3. To determine the absolute uncertainty in the slope:

a. Draw a rectangle with the sides parallel to and perpendicular to the best straight line that just encloses all of the points.

b. The slopes of the diagonals of the rectangle are measured to give a maximum slope and a minimum slope.

c. The absolute uncertainty in the slope is given by:

max slope - min slope

2 n , where n

is the number of data points.

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What has been described above is known as “standard uncertainty theory”. In this system, a

calculated result, accompanied by its uncertainty (the standard deviation s), has the following

properties: There is a 70% probability that the “true value” lies within the ± s of the calculated

value, a 95% probability that it lies within the ± 2s, a 99.7% probability that it lies within ± 3s,

etc. We may therefore state that the “true value” essentially always lies within plus or minus 3

standard deviations from the calculated value. Bear this in mind when comparing your result

with the expected result (when this is known).

Some final words of warning

It is often thought that the uncertainty in a result can be calculated as just the percentage

difference between the result obtained and the expected (textbook) value. This is incorrect. What

is important is whether the expected value lies within the range defined by your result and

uncertainty.

Uncertainties are also sometimes referred to as “errors.” While this language is common practice

among experienced scientists, it conveys the idea that errors were made. However, a good

scientist is going to correct the known errors before completing an experiment and reporting

results. Erroneous results due to poor execution of an experiment are different than uncertain

results due to limits of experimental techniques.

Fig. 1 Graph of extension vs. mass

Mass (kg)

2 3 4 5 6 7

Exten sion(

mm)

4

6

8

10

12

14 Best line

Min. slope Max. slo

pe

9

VERNIER CALIPER

A Vernier scale allows us to measure lengths to a

higher degree of precision than can be obtained with,

say, a millimeter scale. In Fig. 1, a moveable Vernier

scale V is placed next to a millimeter scale M (e.g. on a

meter rule). V is 9mm long and has 10 divisions, each

of length 0.9 mm, so each division on V is shorter than

each division on M by 0.1 mm Fig. 1

Suppose we wish to measure the position on a

meter rule of the right-hand end of an object. V is

positioned as shown in Fig. 2. Clearly the required

reading is somewhere between 24 and 25 mm. To

obtain the fractional part, we note which graduation

on V lines up (or comes closest to lining up) with a

graduation on M. In Fig. 2 it is the 7th, labeled B,

which lines up with C, and the required reading is

therefore 24.7 mm. The reasoning is as follows: Fig. 2

The graduation on V to the left of B is 0.1 mm to the right of the closest graduation on M. The

graduation on V two to the left of B is 0.2 mm to the right of the closest graduation on M, etc.

Therefore the graduation labeled A will be 0.7 mm to the right of the graduation D on scale M.

A tool to measure linear dimensions is the Vernier caliper shown in Fig. 3. It consists of a scale

M graduated in millimeters and attached to a fixed jaw A, and a Vernier scale V on a moveable

jaw B.

Fig.3

Fig. 3

Note that part of the scale M can be seen through an opening in the moveable jaw. When the

jaws are closed, the zero graduations on M and V coincide. The object, C, to be measured is

placed snugly between the jaws by sliding B. The length can then be read from scales M and V.

In Fig. 3, the reading is 2.57 cm. (By counting backwards from the 3 cm graduation, you can see

that the leftmost graduation on V is between 2.5 and 2.6 cm.)

20 mm 30 mm

V

M

A B

CD

Object

1cm0cm 5cm M

A B

C

3

V

cm

B

30 mm 40 mm

V

M

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Lab 1. Electrostatics

Electric charge, like mass, is a fundamental property of the particles that make up matter. However, unlike mass, charge comes in two forms that we label positive (e.g. the charge of a proton) and negative (e.g. the charge of an electron). Normal matter is made up of "neutral" atoms having equal numbers of protons and electrons but, for example, can become negatively charged by gaining electrons, or positively charged by losing electrons. Charged objects of the same sign repel each other whereas those of opposite sign attract each other. In the first part of this experiment, an "electroscope" will be used to demonstrate the existence of the two types of charge and a few of their basic properties. In the second part, the attractive and repulsive forces that charges can exert on each other will be investigated. In the third part, a "Faraday pail" and charge sensor will be used to determine the sign of the charge resulting from rubbing objects together. OBJECTIVES

Demonstrate that a material can acquire a net charge by rubbing it with a dissimilar material.

Demonstrate that either of the two types of charge may be acquired, depending on the material, and demonstrate the forces that charges exert on each other.

Demonstrate that charge can be either transferred to an object or "induced" on an object.

Determine the signs of the charges acquired by rubbing two dissimilar materials together.

MATERIALS

various rods and rubbing cloths Faraday pail and charge sensor electroscope charge separators swivel Labquest Mini

connecting wires computer

PRELIMINARY QUESTIONS

1. If something is "charged," what does that mean?

2. If something is "neutral," what does that mean"

3. What happens if you have two positively charged objects near each other?

4. What happens if you have a positively charged object near a negatively charged one?

PROCEDURE

Part I Demonstrations with the electroscope

The electroscope, shown in Fig. 1, consists of a metal conducting rod with a

metal ball at the upper end and a pair of light, hinged, conducting leaves at

the lower end. The rod is insulated from the electroscope’s metal case by

an insulating stopper. If both leaves acquire either a net positive charge or

a net negative charge, they will separate due to the repulsive forces that the

leaves exert on each other. Fig. 1 shows the situation when the ball, rod,

and leaves have acquired positive charge. Figure 1

Insulator

Metal rod

Conducting leaves

+ + +

+

+

+

+

+

+

+

+

+

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Before attempting each demonstration, touch the knob of the electroscope with your finger to

remove any excess charge it may posses. (Your body acts like a large reservoir for charge to go

to or to come from.) For each demonstration, draw sketches indicating the location of charges on

the different parts of the electroscope and explain your observations.

What to do if you get weak responses. Handling rods can result in contamination that allows

charge to leak away by conduction. Take the rods to a restroom and wash the unpainted length

with soap and water. Dry them thoroughly with paper towel. Back in the lab, dry them further

using a heat gun. Afterwards, do not touch the cleaned part except with the rubbing material.

1. For the following steps, wear a disposable latex glove when holding the painted end of any of the rods. Charge the plastic rod by rubbing it with a piece of cloth, and then touch the rubbed part to the electroscope’s metal ball. The plastic will have acquired a negative charge by the rubbing process.

2. Charge the plastic rod again by rubbing it with a cloth, and then bring it close to the electroscope’s metal ball without touching it.

3. Repeat steps 1 and 2 with the glass rod rubbed with tissue paper ("Kimwipes"). In this case, the glass acquires a positive charge.

4. Bring both the charged plastic rod and glass rod near the metal ball without touching, and see if you can adjust their relative distances from the ball to produce no divergence of the leaves.

5. To charge the electroscope by “induction”, bring the charged plastic rod near the metal ball, but not touching it, and then touch the ball with your finger. Remove your finger and afterwards withdraw the rod. To test the sign of the induced charge on the leaves, once again bring the charged plastic rod near the ball and see if the leaves collapse or diverge further.

Part II Forces that charged objects exert on each other

6. Rub one end of a plastic rod with a cloth and rest it on the swivel. Rub one end of another plastic rod and bring that end close to the rubbed end of the first rod. Observe whether there is attraction or repulsion.

7. Repeat step 6 with two glass rods rubbed with Kimwipes tissue paper.

8. Repeat step 6 with a plastic rod rubbed with cloth on the swivel and a glass rod rubbed with Kimwipes tissue paper brought close to it.

9. Place an uncharged metal rod on the swivel and bring a charged plastic rod close to one end. Observe whether there is attraction or repulsion.

10. Repeat step 9 with an uncharged plastic rod on the swivel. Compare the strength of the force on the plastic rod with that on the metal rod.

Part III Determining the sign of a charge with a Faraday pail

A Faraday pail set-up is shown in Fig. 2. The Faraday pail is the inner cylinder. The outer

cylinder shields the pail from the effects of stray charges in the environment. When, for example,

a positively charged object is placed inside the pail, it attracts electrons through the wire that

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connects the pail to the charge sensor. A

negatively charged object repels electrons

through the wire. In this way, the sensor can

tell the sign of the charged object in the pail.

11. Set up the apparatus as in Fig. 2. Connect

the Labquest unit to the computer. Press and hold the reset button on the charge sensor. This will remove any unwanted charge in the pail or sensor. Repeat this step every time before placing a charged object in the pail

12. Open the Logger Pro file "Electrostatics" in the folder Lab 01. Set the data collection duration to 60 s, and data collection rate to 10 Hz.

13. Press the button on the charge sensor in order to zero it.

14. Discharge the two charge separators by dabbing them on a damp cotton cloth. Start data collection and verify that the charge separators carry no charge by inserting them one at a time into the pail. DO NOT LET THE SEPARATORS TOUCH THE PAIL. Repeat the dabbing process if necessary.

15. Rub the charge separators together, restart data collection, then insert the gray one for about 5 s and then the white one for about 5 s, and finally both together (not touching) for about 5 s.

16. Sketch or print the graph.

ANALYSIS

Part I Demonstrations with the electroscope

1. For each step 1 through 4, sketch the conducting parts of the electroscope and the nearby rod, and show the distribution of charges on each.

2. Explain your observations for steps 1 through 5.

Part II Forces that charged objects exert on each other

3. What force, attraction or repulsion, do charges having the same sign exert on each other?

4. What force, attraction or repulsion, do charges having opposite signs exert on each other?

5. How do you explain your observations in steps 9 and 10?

Part III Determining the sign of a charge with a Faraday pail

6. What were the signs of the charge for the gray and white charge separators?

7. What was the net charge on the pair of separators?

Figure 2

To Lab Quest

13

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Lab 2. Coulomb's Law

The electrostatic forces which you observed in Lab 1 were studied in detail by Coulomb in 1784. His experiments resulted in the empirical law named after him. It describes the forces that two small, particle-like, charged objects exert on each other, forces that depend on the magnitudes of the charges, q1 and q2, as well as the distance r between the charged particles. See Fig. 1. To attempt to explore Coulomb's Law using physical apparatus is fraught with difficulty, especially in south Florida. For this reason, you will be using a computer simulation instead.

Figure 1 OBJECTIVES

• Determine how the forces on the particles depend on their charges.

• Determine how the forces on the particles depend on the distance between them.

• Determine whether Newton's 3rd law is applicable to these forces.

• Obtain a value for the Coulomb law constant. MATERIALS

computer PRELIMINARY QUESTIONS

1. Why do you think that exploring Coulomb's law with physical apparatus is "fraught with difficulty, especially in south Florida?"

2. How would you expect the forces to depend on the magnitude of either charge?

3. How would you expect the forces to depend on the distance between the particles? Would it increase or decrease as the distance increases?

4. Do the signs of the charges play a role? Explain.

5. Do you think that the magnitude of the force on the larger charge is bigger than that on the smaller charge?

PROCEDURE

1. Open simulation “Electrostatic” in folder Lab02.

2. Learn how to move the charges, change their magnitude and sign, and change the distance between them. Note qualitatively how the forces are affected by these changes. You can also move the ruler. It's 10 m long, so the main divisions are spaced at 1 m, the same as the spacing of the grid lines.

q1 q2

r

15

3. Keeping the distance between the charges fixed, conduct an experiment to determine how the forces vary with the magnitudes of the charges. Try keeping one charge fixed and record the force as the other charge is varied. Then try several different combinations so that the product of the two charges, q1q2, covers a large range. You should obtain enough data to fill Table 1. Also record the distance between the charges in the table.

4. Open Logger Pro file "Coulomb's Law" in folder Lab 02. Enter your data, create a new column containing the product of the two charges, q1q2, then plot a graph of force versus q1q2.

5. Keeping the magnitudes of the charges fixed, perform an experiment to determine how the forces vary with the distance between the charges. Obtain a set of measurements for distances ranging from 2 m to 12 m in 1 m increments. Record your data in Table 2, along with the values of the two charges.

6. Enter your data in Logger Pro and plot a graph of force versus the distance, r, between the charges.

7. For each value of r, enter the values of a suitable function of r in the last column in data set 2 which you think will result in a linear plot of force versus this new function of r. Check that the new plot is indeed linear.

ANALYSIS

1. What did you observe about the magnitudes of the forces on the two charges. Were they the same or different? Does your answer depend on whether the charges were of the same magnitude or different? How does this relate to Newton's 3rd law?

2. What did you observe about the directions of the two forces? How did the directions depend

on the signs of the charges?

3. Print your three graphs.

4. The graph of force vs. q1q2 should be linear. To fit a line to this data, click and drag the mouse across the linear region, then click Linear Fit, .

4. Combine the slope of the line with the value of r in order to obtain the value (plus units) of the Coulomb law constant.

5. What was the function of r that resulted in your third graph being linear?

6. Combine the slope of this graph with the values of q1 and q2 to again obtain the value (plus units) of the Coulomb law constant.

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DATA TABLES

Table 1 Distance between charges, r = m

q1 (C) q2 (C) Force (N)

Table 2 q1 = C q2 = C

Distance, r (m) m

Force (N)

17

Lab 3. Electric Field and Potential

Coulomb's Law describes the force that one charged particle exerts on a second charged particle. A more useful description includes the role of the electric field. It is preferable to say that the first particle produces an electric field in the space around it, and if a second particle is placed in this space, the field exerts a force on it. The strength of the field, E , at the location where the second particle was placed is defined as the force on that particle divided by its charge. A second related field that characterizes the space is electric potential, V. The relation between the two is that E is the "gradient" of V (the rate of change of V with position).

In this experiment, you will be mapping the potential in the space around a pair of charged objects and determining what information can be extracted regarding the associated electric field.

OBJECTIVES

Measure the potential at different points in the space surrounding different pairs of charged objects.

Generate, and familiarize yourself with the concept of, "equipotential lines."

Learn how to deduce E from the equipotential lines and the spacing between them. MATERIALS

glass try battery different shaped conductors connecting wires multimeter grid paper

PRELIMINARY QUESTIONS

1. What is meant by "voltage?"

2. If E is the gradient of potential, then 1 N/C should be the same as 1 V/m. Show that this is true. You may need to look up the definition of the volt.

3. What is the value of E inside a conductor, charged or uncharged?

4. What can you say about the potential inside a conductor, charged or uncharged?

INITIAL SET UP

1. Place the two pieces of L-shaped aluminum at opposite ends of the tray as shown in Fig. 1 to simulate two parallel plates. Three sheets of tear-out grid paper are provided in this manual following page 17. Place the tray on the grid paper and adjust the positions of the plates so that the vertical surfaces facing each other line up with the markings on the grid.

Figure 1

18

2. Add water to the tray leaving about a quarter inch of the plates above the surface.

3. Connect the negative terminal of the 9 V battery to the right plate. The connecting clip must not touch the water. For added stability, thread the connecting wire upwards through the slot in the tray handle.

4. You will be measuring potential with the multimeter which you should set to DC voltage (V) and the smallest range which exceeds 9 V. This will give you maximum sensitivity. The probes should be connected to voltage and ground terminals of the meter. Connect the ground probe to the negative plate and place the other probe in the water. The meter will record the potential difference between the probes. However, if we arbitrarily assign a potential of zero for the negative plate, then the reading on the meter will be the potential at the location where the other probe is placed.

5. CHECK WITH YOUR TA before making the final connection of the positive terminal of the battery to the left plate. Remember you are dealing with electricity and water which is a conductor, albeit a weak one. You have now established a potential of 9 V for the left plate relative to 0 V for the right plate. Check that this is so by touching the probe to each plate.

PROCEDURE

1. Place the probe vertically in the water and note on the meter how the potential changes as you move the probe from point to point.

2. Map the 2 V equipotential line by locating as many points as possible where the meter reads 2 V. Make a note of the coordinates on the grid paper where this occurs. Repeat for the 3, 4, 5, 6, and 7 V equipotential lines.

3. Disconnect the battery, then remove the grid paper and draw and label the equipotential lines.

4. Remove the parallel plates and repeat the above procedures with the two metal cylinders. This will be an approximate simulation of two oppositely charged particles. Center the cylinders over the circular markings on the grid paper so that you can map the equipotential lines around the cylinders as well as between them.

5. Remove the left cylinder and replace it with one of the plates. This will be an approximate

simulation of a charged particle in front of a flat plate. Map the equipotential lines as before.

ANALYSIS

1. On each of your equipotential maps, draw some electric field lines with arrow heads indicating the direction of the field. (Hint: At what angle do field lines intersect equipotential lines?) Draw sufficient field lines that you can "see" the electric field.

2. Describe the electric field between the parallel plates. Are there regions where it appears uniform? non-uniform? What is the value of E midway between the centers of the plates?

3. From the "density" of the electric field lines seen in the second two maps, how can you tell where E is large and where it is small?

4. From the spacing between the equipotential lines seen in the second two maps, how can you tell where E is large and where it is small?

19

20

21

22

Lab 4. Capacitors

A capacitor is any two conductors separated by an insulator. If a potential difference, V, is

established between the conductors, charges +q and –q appear on the conductors. The

relationship between q and V is q = VC, where the constant C is the capacitance of the capacitor

measured farads, F, (1 F = 1 C/V). The capacitance depends on size, shape, and location of the

conductors as well as the insulating material. In this lab, we first build a parallel plate capacitor

and then investigate combinations of capacitors as well as the charging/discharging

characteristics of capacitors. A parallel plate capacitor consists of two flat conducting plates

placed on top of each other, but separated by an insulating layer. The capacitance of a parallel

plate capacitor is given by

d

A C 0

 =

where  is the dielectric constant of the insulator, 0 is the permittivity of free space, A is the

area of either plate, and d is the separation distance between the plates.

To study the charging/discharging properties of a capacitor, we’ll build an RC circuit with a

capacitor, resistor, and battery. We’ll connect a charged capacitor to the resistor and monitor the

charge flowing off one of the plates, through the resistor, and onto the other plate. OBJECTIVES

• Build and investigate the capacitance of a parallel plate capacitor.

• Investigate the capacitance of capacitors connected in series and in parallel

• Measure an experimental time constant of a resistor-capacitor circuit.

• Compare the time constant to the value predicted from the component values of the resistance and capacitance.

MATERIALS

aluminum foil resistor meter stick power supply multimeter current probe capacitors Labquest Mini

Vernier caliper computer

PRELIMINARY QUESTIONS

1. A good analogy to charging a capacitor would be filling a scuba tank with compressed air. What would be the quantities equivalent to q, V, and C in the relation q = VC?

2. In simple terms, why would you expect the capacitance of a capacitor to be proportional to the plate area?

3. Why would you expect the capacitance of a capacitor to be inversely proportional to the distance between the plates?

23

PART 1: BUILD A CAPACITOR You can build a parallel plate capacitor out of two sheets of aluminum foil separated by a piece of paper. We’ll use textbook pages as the separator since it is easy to slip the aluminum foil between any number of pages, thus varying the separation distance. To ensure the aluminum foil sheets have uniform separation, place a weight on top of the book. Be careful not to “short out” the sheets of aluminum foil when you connect the meter leads to the sheets. That is, don’t let them touch each other.

PROCEDURE

1. Take two pieces of aluminum foil approximately the size of your textbook and measure their area. You may want to add small “tabs” for connecting to the multimeter leads. Place them in your textbook separated by 10 pages. They should be carefully aligned with each other. Note that if the areas are slightly different, the area that should be recorded in the data table is the area of overlap. You may want to add small “tabs” for connecting to the multimeter leads. Place a weight on the textbook

2. Attach two leads with alligator clips to the tabs. At your station is a meter that can measure capacitance. Select the capacitance measurement function ( symbol) on the meter. Attach the other ends of the leads to the meter and take a measurement of the capacitance.

3. Fill in the data table with your values.

4. To explore the relationship of capacitance to the separation distance, change the number of pages between the foils. You want to make an additional four (or more) measurements and record them in the table. Make sure to place the weight on the book for each measurement. Decide how to vary the numbers of pages, considering how the capacitance depends on separation distance.

5. To explore the relationship of capacitance to area, reduce the area of both pieces of foil equally, insert them into the book, and record your measurements in the table. You should carry out at least two additional measurements to study the trend. Decide how to vary the size of the foil. Again, consider how to optimize the measurements.

6. Estimate the thickness of the pages by using a Vernier caliper to measure a large number of pages and then determine the average values for the thickness. You may want to make several measurements and average the results.

ANALYSIS

1. Open the Logger Pro file "DIY-capacitor" in folder Lab 04, enter your data and plot a graph of the measured capacitance vs. the distance between the plates for the same plate area.

2. How does the capacitance depend on separation? Does it follow a straight line? Does it follow the trend you expect? Why or why not?

3. What should be plotted on the x and y axes to produce a straight line graph? Plot another graph to check your prediction. (The last column in the data table can be used to enter the appropriate values.)

24

4. Plot a graph of the measured capacitance vs. the area of the plates for the same plate separation.

5. How does the capacitance depend on area? Does it follow a straight line? Does it follow the trend you expect? Why or why not?

6. Using the slope of this graph, together with the distance between the plates, determine the dielectric constant of paper. Find a value for the dielectric constant of paper on the Web or elsewhere and compare to your measured value. (Note that different types of paper could have different dielectric constants.)

PART 2: CAPACITORS IN SERIES AND IN PARALLEL

1. Use the multimeter to measure the capacitances of three capacitors

2. Connect the capacitors in series and measure the capacitance of the combination.

3. Connect the capacitors in parallel and measure the capacitance of the combination.

ANALYSIS

1. Calculate the capacitance of the series combination of capacitors and compare it with what you measured.

2. Calculate the capacitance of the parallel combination of capacitors and compare it with what you measured.

PART 3: INVESTIGATE DISCHARGING OF A CAPACITOR

A capacitor that has been previously charged by connecting it to a battery, can be discharged by connecting it to a resistor (a conductor that impedes the flow of electrons to a greater or lesser extent), a so-called RC circuit. As the charge on the plates decreases, so too does the voltage between the plates (because q = VC). Since it this voltage that drives the discharge, the rate of flow of electrons decreases exponentially with time. If we plot a graph of the rate of flow of charge (current) vs. time, the area under the curve is equal to the total amount of charge that has flowed which, if we wait until the flow has stopped, must be the same as the charge that was initially on the plates.

Fig. 1a Rate of flow of charge as function of time Fig. 1b Bar chart approximation of Fig. 1a

25

Why is the area under the curve equal to the total amount of charge that has flowed? Hint: To answer this question, consider the bar chart in Fig. 1b which approximates the actual curve in Fig 1a. During each interval, t, the amount of charge that has flowed is equal to the rate of flow (height of column) multiplied by t (width of column), i.e. the area of the column.

PROCEDURE

Fig. 2 RC circuit.

1. Connect a series circuit of the resistor, capacitor, current probe and battery as shown in Fig. 2. Make sure the capacitor and current probe terminals labeled + and – are as shown in Fig. 2, and that the battery pack's red and black terminals are as shown. One end of the connecting wire, labeled A, from the resistor is shown disconnected. If the end A is connected to the battery's positive terminal, B, the battery will charge the capacitor through the resistor. If, subsequently, the end A is connected to the terminal C, the battery pack is eliminated from the circuit, and the capacitor will discharge through the resistor.

2. We now want to obtain a graph of the rate of flow of charge (current) as the capacitor discharges. Plug the third current probe lead into the Labquest unit, and plug the Labquest into a USB port on the computer.

3. Open the Logger Pro file "Capacitor" in folder Lab 04. A graph will be displayed. The vertical current axis of the graph should be rescaled, if necessary, from 0 to 0.1 amps. The horizontal axis has time scaled from 0 to 10 s. With end A still disconnected, zero the current probe by clicking the "Set zero point" button  on the toolbar.

4. Connect the end A of the connecting wire to the battery's positive terminal, B. The capacitor will become fully charged after about 10 seconds.

5. With A still connected to B, use the multimeter to measure the voltage between the plates. To do so, set the multimeter to DC volts, and then touch the multimeter probes to the terminals of the capacitor. Calculate the charge on the capacitor from the relation q = VC.

6. Disconnect the end A of the connecting wire from B (the capacitor will retain its charge), click to begin data collection, and immediately connect the end A to terminal C.

26

7. You should obtain a curve similar to Fig. 1a, but with a zero current portion for the period before A was connected to C. Repeat steps 4 to 6 if necessary to obtain a good graph. The curve should have reached baseline. If necessary, rescale the horizontal time axis.

ANALYSIS

1. Using only the portion of the graph from the peak out to baseline (~ 10 seconds), determine the area under the curve using the integration button. Record it as the total charge that has flowed.

2. Print a copy of the graph of current flowing as a function of time.

3. How did the initial charge on the capacitor compare with the total charge that flowed?

4. How quickly the capacitor discharges depends, as you will learn later, on the "time constant" of the RC circuit. It is defined as the time taken for the current to decrease to 1/e of the initial value. (e = 2.718 is the base of natural logarithms.) From your graph, determine the time constant and enter the value in the table.

5. Theoretically, the time constant, t, can be shown to be equal to R times C (t = RC). If R is in ohms and C is in farads, t will be in seconds. Calculate the time constant, enter the value in the table, and compare it with the value from your graph.

27

DATA TABLES

PART 1

Separation (m) Length (m) Width (m) Area (m2) Capacitance

PART 2

Capacitance (F)

(measured)

Capacitance (F)

(theoretical)

C1

C2

C3

Series combination

Parallel combination

PART 3

Initial charge on capacitor (C)

Total charge that flowed (C)

Time constant, measured (s)

Time constant, theoretical (s)

28

Lab. 5 Ohm’s Law & Resistance

The fundamental relationship among the three important electrical quantities current, voltage, and resistance was discovered by Georg Simon Ohm. The relationship and the unit of electrical resistance were both named for him to commemorate this contribution to physics. One statement of Ohm’s law is that the current through a resistor is proportional to the voltage across the resistor. In this experiment you will test the correctness of this law in several different circuits using a Current & Voltage Probe System and a computer.

These electrical quantities can be difficult to understand because they cannot be observed directly. To clarify these terms, we can make the comparison between electrical circuits and water flowing in pipes. Here is a chart of the three electrical units we will study in this experiment.

Electrical Quantity Description Unit

Water Analogy

Potential Difference or

Voltage

Potential energy

difference/unit charge of a

charge at two points in a

circuit.

Volt (V)

1 V = 1 J/C

Water pressure difference

between two points in a pipe

Current Rate of flow of charge through

a conductor.

Ampere (A)

1 A = 1 C/s

Rate of flow of water

through a pipe

Resistance A measure of how difficult it is

for charged particles to flow

through a conductor.

Ohm () A measure of how difficult it is for water to flow

through a pipe.

OBJECTIVES

• Determine the mathematical relationship between current, potential difference, and resistance in a simple circuit.

• Compare the potential difference vs. current behavior of a resistor to that of a light bulb and light emitting diode (LED).

MATERIALS

computer two resistors (about 56 and 82 ) Labquest Mini connecting wires adjustable 6-volt DC power supply light bulb (6.3 V) current probe & voltage probe LED

PRELIMINARY QUESTIONS

1. A TV news reporter once stated that a person was electrocuted "when 20,000 volts of electricity surged through his body." What is wrong with this description? What was it that "surged" through his body?

2. Do you expect the resistance of a light bulb to remain constant as the current through it is increased and the filament goes from red-hot to white-hot? Explain why or why not.

29

3. The definition of the resistance of a conductor is R = V/I, where V is the potential difference between its ends and I is the resulting current through it. Ohm's Law, as an equation, states that V = IR. The two equations look the same. What is the difference?

PRELIMINARY SETUP

The resistance of a resistor is often indicated by a series of colored bands painted on the body of the resistor. The colors of the bands indicate numbers: black = 0, brown = 1, red = 2, orange = 3, yellow = 4, green = 5, blue = 6, violet = 7, gray = 8, white = 9. A "tolerance" band is indicated by silver (±10%) or gold (±5%). If you orient the resistor with the tolerance band on the right, the two leftmost bands give the first and second digits, and the third band gives the number of following zeros. So if the band colors are red, green, black, and silver, the resistance is 25  and the tolerance is ± 10%.

1. WITH THE POWER SUPPLY SWITCHED OFF, connect the power supply, 56  resistor, wires, and clips as shown in Figure 1. Take care that the positive lead from the power supply's DC output and the red terminal from the Current and Voltage Probe are connected as shown in Figure 1. Note: Attach the red connectors electrically closer to the positive side of the power supply.

2. Connect the outputs from the current probe and voltage probe to the Labquest unit and connect the Labquest unit to the computer.

3. Open the Logger Pro file "Ohm's Law" in the folder Lab 05. A graph of potential difference vs. current will be displayed. The horizontal axis is scaled from 0 to 0.6 A. The Meter window displays potential and current readings.

4. Click the "Set zero point" button  on the toolbar. A dialog box will appear. Select the two sensors and click "OK." This sets the zero for both probes with no current flowing and with no voltage applied.

5. HAVE YOUR INSTRUCTOR CHECK YOUR SET-UP BEFORE PROCEEDING.

6. Turn the control on the DC power supply to 0 V and then turn on the power supply. Slowly increase the voltage to 6 V. Monitor the Meter window in Logger Pro and describe what happens to the current through the resistor as the potential difference across the resistor changes. If the voltage doubles, what happens to the current? What type of relationship do you believe exists between voltage and current?

Power supply+ -

I Resistor

BlackRed

Current probe

Voltage probe

Red Black

To LabquestVoltage probe

Figure 1

30

PROCEDURE

1. Record the value of the resistor in the data table.

2. Make sure the power supply is set to 0 V. Monitor the voltage and current. When the readings are stable, record the voltage and current in the data table.

3. Increase the voltage on the power supply by approximately 0.5 V. Again when the readings are stable, record the voltage and current in the data table.

4. Repeat step 3 until you reach a voltage of 6.0 V.

5. In LogPro, enter current and voltage from the data table in the columns 'Current (graph)' and 'Potential (graph),' respectively. Print a copy of the graph.

6. Are the voltage and current proportional? Click the Linear Regression button, . Record the slope and intercept in the data table. Click the Curve Fit button, . Choose 'Proportional Fit.' Record the slope and error in the data table.

7. Repeat Steps 1 – 6 using an 82  resistor.

8. Replace the resistor in the circuit with a 6.3-V light bulb and repeat Steps 2 – 5, but this time plot current on the y axis and voltage on the x axis. (Double left click on the graph and make changes under "Axes Options'.) Print a copy of the graph. Calculate the effective resistance for each pair of measurements.

9. You are provided with a transparent box containing a light emitting diode ( LED) in series with a protective resistor. Turn off the power supply and set up the circuit shown in Figure 2. Make sure you connect the power supply's positive terminal to the red socket on the box. Connect the red lead from the voltage probe to the red socket on the box and the black lead to the central tab on the box. You will then be measuring the voltage across the LED only.

10. Turn on the power supply and make a series of voltage and current measurements as before, but at 0.2 V intervals once the current begins to increase. Plot and print a graph as you did for the light bulb (current on the y axis, voltage on the x axis).

Figure 2

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ANALYSIS

1. As the voltage between the ends of the resistor increased, the current through the resistor increased. If the current is proportional to the voltage, the data should lie on a straight line passing through the origin. For the two resistors, how close is the y-intercept to zero? Is there a proportional relationship between voltage and current? If so, write the equation for each resistor in the form potential difference = constant  current. (Use a numerical value for the constant.)

2. Compare the constant in each of the above equations to the resistance of each resistor.

3. Resistance, R, is defined using R = V/I where V is the voltage across a resistor, and I is the current. R is measured in ohms (), where 1  = 1 V/A. The constant you determined in each equation should be similar to the resistance of each resistor. However, resistors are manufactured such that their actual value is within a tolerance. Examine your resistors' color codes to determine the tolerance of the resistors you are using. Calculate the range of values for each resistor. Does the constant in each equation fit within the appropriate range of values for each resistor?

4. Do your resistors follow Ohm’s law? Base your answer on your experimental data.

5. Describe what happened to the current through the light bulb as the voltage increased. Was the relationship linear? Determine the resistance at each voltage and enter the results in the data table. Describe what happened to the resistance as the voltage increased. Since the bulb gets brighter as it gets hotter, how does the resistance vary with temperature?

6. Does your light bulb obey Ohm’s law? Base your answer on your experimental data.

7. Describe what happened to the current through the LED as the potential difference increased. Was the relationship linear? Determine the resistance for each voltage and enter the results in the data table. Describe what happened to the resistance as the voltage increased.

8. For the maximum voltage settings in each case, calculate the corresponding electrical power, P, being consumed by the light bulb and LED. (Recall that P IV= .) P represents the rate at which electrical energy is being converted into other forms, such as light and thermal energy. Which device appears to be more efficient at producing light?

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DATA TABLES

56  resistor 82  resistor Light bulb

Voltage (V) Current (A) Voltage (V) Current (A) Voltage (V) Current (A) Resistance ()

Slope of

regression line

(V/A)

Intercept

(V)

Slope of

proportional fit

(V/A)

Error in

proportional fit

()

Resistor ± 

Resistor ± 

33

LED

Voltage (V) Current (A) Resistance ()

Device Power (W)

Light bulb

LED

34

Lab 6. Series and Parallel Circuits

Components such as resistors and capacitors in an electrical circuit are in series when they are connected one after the other, so that the same current flows through all of them. Components are in parallel when they are all connected between the same pair of points. Series and parallel combinations function differently. You may have noticed the differences in electrical circuits you use. When using some decorative holiday light circuits, if one lamp burns out, the whole string of lamps goes off. These lamps are in series. When a light bulb burns out in your house, the other lights stay on. Household lamps and other electrical devices are normally in parallel.

You can monitor these circuits using a Current and Voltage Probe System and see how they operate. One goal of this experiment is to study circuits made up of two resistors in series or parallel. You can then use Ohm’s law to determine the equivalent resistance of the two resistors.

OBJECTIVES

• To study current flow in series and parallel circuits.

• To study voltages in series and parallel circuits.

• Use Ohm’s law to calculate equivalent resistance of series and parallel circuits.

Series Resistors

Parallel Resistors

MATERIALS

computer two 56- resistors Labquest Mini two 82- resistors low-voltage DC power supply momentary-contact switch current probe & voltage probe connecting wires

PRELIMINARY QUESTIONS

1. Based on what you know about electricity, hypothesize about how series resistors would affect current flow. What would you expect the effective resistance of two equal resistors in series to be, compared to the resistance of a single resistor?

35

2. Using what you know about electricity, hypothesize about how parallel resistors would affect current flow. What would you expect the effective resistance of two equal resistors in parallel to be, compared to the resistance of one alone?

3. For each of the two resistor values you are using, note the tolerance rating. Tolerance is a percent rating, showing how much the actual resistance could vary from the labeled value. This value is labeled on the resistor or indicated with a color code (below). Calculate the range of resistance values that fall in this tolerance range. The color code uses colors to indicate numbers: black = 0, brown = 1, red = 2, orange = 3, yellow = 4, green = 5, blue = 6, violet = 7, gray = 8, white = 9. The tolerance colors are silver = 10% and gold = 5%. If you orient the resistor with the tolerance band on the right, the two leftmost bands give the first and second digits, and the third band gives the number of following zeros. So if the band colors are red, green, brown, and silver, the resistance is 250 , and the tolerance is ± 10%.

Resistance of resistor

Tolerance

Minimum resistance

Maximum resistance

() (%) () ()

PROCEDURE

Part I Series Circuits

Figure 1

1. Plug the voltage probe and both current probes into the Labquest interface before opening the LogPro file. Leave the three probes plugged in even though not all of them are used for various parts of the experiment. Connect the series circuit shown in Fig. 1 using the 56- resistors for resistor 1 and resistor 2. Note that it is easier to connect the rest of the circuit

Red Black

Power supply+ -

R BA

R

BlackRed

I

To Labquest Voltage probe

Current probe

36

without the voltage probe. Finally connect the voltage probe and note that it is used to measure the voltage applied to the series combination of resistors. The red terminal of the current probe should be toward the + terminal of the power supply's DC output.

2. Connect the current probe and the voltage probe to the Labquest unit and connect the Labquest unit to the computer.

3. Open the Logger Pro file "Parallel-series" in folder Lab 06. Current and voltage readings will be displayed in a Meter window.

4. With the power supply switched off, click the "Set zero point" button  on the toolbar. A dialog box will appear. Select the two sensors and click "OK." This sets the zero for both probes with no current flowing and with no voltage applied.

5. HAVE YOUR INSTRUCTOR CHECK YOUR SET-UP BEFORE PROCEEDING Switch on the power supply and adjust the voltage to 3 V. For this part of the experiment, you do not even have to click on the button. You can take readings from the Meter window at any time. To test your circuit, briefly press on the switch to complete the circuit. Both current and voltage readings should increase. If they do not, recheck your circuit.

6. Press on the switch to complete the circuit again and read the current (I) and total voltage (VTOT). Record the values in the data table.

7. Connect the leads of the voltage probe across resistor 1. Press on the switch to complete the circuit and read this voltage (V1). Record this value in the data table.

8. Connect the leads of the voltage probe across resistor 2. Press on the switch to complete the circuit and read this voltage (V2). Record this value in the data table.

9. Repeat Steps 5 – 8 with an 82- resistor substituted for resistor 2.

10. Repeat Steps 5 – 8 with an 82- resistor used for both resistor 1 and resistor 2.

Part II Parallel circuits

11. Connect the parallel circuit shown in Fig. 2 using 56- resistors for both resistor 1 and resistor 2. The voltage probe is used to measure the voltage applied to both resistors. The red terminal of the current probe should be toward the + terminal of the power supply's DC output. The current probe is used to measure the total current supplied by the power supply.

Power supply+ -

BlackRed

I

R 2

1R

Red Black

To Labquest Voltage probe

Black Red

Current probe

Figure 2

37

12. As in Part I, you can take readings from the Meter window at any time. To test your circuit, briefly press on the switch to complete the circuit. Both current and voltage readings should increase. If they do not, recheck your circuit.

13. Press the switch to complete the circuit again and read the total current (I) and total voltage (VTOT). Record the values in the data table.

14. Connect the leads of the voltage probe across resistor 1. Press on the switch to complete the circuit and read the voltage (V1) across resistor 1. Record this value in the data table.

15. Connect the leads of the voltage probe across resistor 2. Press on the switch to complete the circuit and read the voltage (V2) across resistor 2. Record this value in the data table.

16. Repeat Steps 13 – 15 with an 82- resistor substituted for resistor 2.

17. Repeat Steps 13 – 15 with an 82- resistor used for both resistor 1 and resistor 2.

Part III Currents in Series and Parallel circuits

18. For Part III of the experiment, you will use two current probes. Connect the series circuit shown in Fig. 3 using the 56- resistor and the 82- resistor. The current probes will measure the current flowing into and out of the two resistors. The red terminal of each current probe should be toward the + terminal of the power supply's DC output.

19. Connect the second current probe to the Labquest and zero both current probes as before.

I I

+ -

10 5056  82 

Power supply

To Labquest

Current probe

Current probe

Figure 3

20. For this part of the experiment, you will make a graph of the current measured by each probe as a function of time. You will start the graphs with the switch open, close the switch for a few seconds, and then release the switch. Before you make any measurements, think about what you would expect the two graphs to look like. Sketch these graphs showing your prediction. Note that the two resistors are not equal.

21. Click on the button, wait a second or two, then press on the switch to complete the circuit. Release the switch just before the graph is completed.

38

22. Select the region of the graph where the switch was on by dragging the cursor over it. Click on the Statistics button, , and record the average current in the data table. Determine the average current in the second graph following the same procedure.

23. Connect the parallel circuit as shown in Fig. 4 using the 56- resistor and the 82- resistor. The two current probes will measure the current through each resistor individually. The red terminal of each current probe should be toward the + terminal of the power supply. Zero the current probes as before.

To Labquest

+ -

I

I

+ -

68

50

I 56 

82 

Power supply

Current probe

Current probe

Figure 4

24. Before you make any measurements, sketch your prediction of the current vs. time graphs for each Current Probe in this configuration. Assume that you start with the switch open as before, close it for several seconds, and then open it. Note that the two resistors are not identical in this parallel circuit.

25. Click on the button and wait a second or two. Then press on the switch to complete the circuit. Release the switch just before the graph is completed.

26. Select the region of the graph where the switch was on by dragging the cursor over it. Click on the Statistics button, , and record the average current in the data table. Determine the average current in the second graph following the same procedure.

ANALYSIS

1. Examine the results of Part I. What is the relationship between the three voltage readings: V1, V2, and VTOT?

2. Using the measurements you have made above and your knowledge of Ohm’s law, calculate the equivalent resistance (Req) of the circuit for each of the three series circuits you tested.

3. Study the equivalent resistance readings for the series circuits. Can you come up with a rule for the equivalent resistance (Req) of a series circuit with two resistors?

4. For each of the three series circuits, compare the experimental results with the resistance calculated using your rule. In evaluating your results, consider the tolerance of each resistor by using the minimum and maximum values in your calculations.

5. Using the measurements you have made above and your knowledge of Ohm’s law, calculate the equivalent resistance (Req) of the circuit for each of the three parallel circuits you tested.

39

6. Study the equivalent resistance readings for the parallel circuits. Devise a rule for the equivalent resistance of a parallel circuit of two resistors.

7. Examine the results of Part II. What do you notice about the relationship between the three voltage readings V1, V2, and VTOT in parallel circuits.

8. What did you discover about the current flow in a series circuit in Part III?

9. What did you discover about the current flow in a parallel circuit in Part III?

10. If the two measured currents in your parallel circuit were not the same, which resistor had the larger current going through it? Why?

40

DATA TABLES

Part I: Series circuits

R1 ()

R2 ()

I (A)

V1 (V)

V2 (V)

Req ()

VTOT (V)

1 56 56

2 56 82

3

82 82

Part II: Parallel circuits

R1 () R2 () I (A) V1 (V) V2 (V) Req ()

VTOT (V)

1 56 56

2 56 82

3

82 82

Part III: Currents

R1 () R2 () I1 (A) I2 (A)

1 56 82

2 56 82

41

Lab 7. Magnetic Force on Moving Charges

Whereas an electric field E exerts a force qE on a charge q placed in the field, a magnetic field,

B only exerts a force on a charge if the charge is moving. The force is given by F qv B=  . An

alternative expression applies when the moving charges constitute a current I in a straight length

of a conductor: F I B=  where is in the direction of I . This relationship will be explored

through the use of a "current balance." You may have learned the "right-hand rule" for a cross

product to give you the direction of F . Instead, you can use the "bottle cap rule." (Point your arm

in the direction of the first vector, then rotate your arm towards the direction of the second

vector. Imagine applying that rotation to a bottle cap. The direction in which the bottle cap

advances, i.e. tightens down or loosens up, gives the correct direction.)

OBJECTIVES

• Investigate the magnetic force on the current in a conductor and what it depends on.

• Understand the right-hand rule, or bottle cap rule. MATERIALS

Current balance apparatus connecting wires Power supply or battery Labquest Mini computer

meter stick high current probe

PRELIMINARY QUESTIONS

1. If you want to maximize the magnetic force on a current in a conductor, how should you orient the current relative to the magnetic field?

2. If you want the force to be zero, in what two directions could you orient the current relative to the magnetic field?

PRELIMINARY SETUP

Figure 1

42

Figure 2

1. Set up the apparatus as shown in Figs. 1 and 2. Note that the small magnets need to be arranged with the same polarity, i.e. white poles align with white and red poles align with red. Open the Logger Pro file "Magnetic force" in the folder Lab 07.

2. Zero the balance, then place the magnet assembly on the pan of the balance.

3. Connect the power supply, which must be switched off, and current probe as shown in Fig. 2. In the following experiments, the power supply should be switched off except when taking readings. This will prevent excessive heating of the current loops and wiring.

4. Note that you have a supply of "current loops" that plug into the end of the Main Unit. When you install one, make sure that you adjust the position of the Main Unit and/or the Magnet Assembly so that the lower, horizontal conductor on the current loop is between the poles of the Magnet Assembly, but not touching it. The effective lengths are shown below. (Note that SF41 and SF42 have two turns of conductor and therefore a longer effective length.)

Current Loop Length

Current Loop Effective Length (cm)

SF 40 1.2

SF 37 2.2

SF 39 3.2

SF 38 4.2

SF 41 6.4

SF 42 8.4

5. Note also that the magnetic field produced by the Magnet Assembly can be varied by adding

or removing individual magnets. Initially it should contain all the magnets.

PROCEDURE

EXPERIMENT 1. FORCE VS. CURRENT

1. Install the SF 38 (4.2 cm) current loop.

2. Record the reading on the balance in the first row (current = 0) of the first data table.

3. Before switching on the current, make a prediction about whether the balance reading will increase or decrease when you switch it on. To assist you in this, recall that B points from the north to south pole of a magnet. The direction of I can be found by tracing the circuit. (Current flows out of the positive terminal of the power supply.) Finally, the force on the balance is the reaction to the force on the current loop. We want the balance reading to increase when the current is turned on. If your prediction is that it will decrease, reverse the connections to the main unit.

4. With the power supply set to the lowest output, switch it on and adjust the current to 0.5 A. Record the reading on the balance in the data table.

5. Increase the current in 0.5 A steps to a maximum of 5.0 A, recording the balance reading each time.

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EXPERIMENT 2. FORCE VS. LENGTH

6. Switch off the power supply and recheck the balance reading, recording the value in the second data table.

7. Switch on the power supply and set the current at 2.0 A. Record the balance reading, then switch off the power supply.

8. Repeat step 7 for each of the 6 current loops.

EXPERIMENT 3. FORCE VS. MAGNETIC FIELD

9. Remove all but one of the individual magnets from the Magnet Assembly and install the SF 38 (4.2 cm) current loop.

10. Switch off the power supply and recheck the balance reading, recording the value in the third data table.

11. Switch on the power supply and set the current at 2.0 A. Record the balance reading, then switch off the power supply.

12. Repeat steps 10 and 11 for 2, 3, 4, 5, and 6 individual magnets in the Magnet Assembly.

ANALYSIS

1. Convert the balance readings (mass in grams) to force (N) for each data table. To do so, you first need to subtract the balance reading when the current was zero.

2. Create graphs for each experiment. Force should be on the y axis and current, length, or number of magnets should be on the x axis. Include linear regression lines. Print the graphs.

3. For the graph of force versus current, what is the relationship between the two variables? Does it confirm the theoretical prediction?

4. For the graph of force versus length, what is the relationship between the two variables? Does it confirm the theoretical prediction?

5. For the graph of force versus number of magnets, what is the relationship between the two variables? From your results, does it look as if the magnetic field is proportional to the number of magnets used? Explain why or why not.

44

DATA TABLES

Current (A)

Mass (grams)

Force (N)

Current (A)

Mass (grams)

Force (N)

0.0 3.0

0.5 3.5

1.0 4.0

1.5 4.5

2.0 5.0

2.5

Mass with I = 0 _____________ grams

Length (cm)

Mass (grams)

Force (N)

1.2

2.2

3.2

4.2

6.4

8.4

Number of magnets

Mass with I = 0 (grams)

Mass with I = 2A

Force (N)

1

2

3

4

5

6

45

Lab 8. Magnetic Field of a Solenoid

A solenoid is made by taking a tube and wrapping it with many turns of wire. A metal Slinky is the same shape and will serve as our solenoid. When a current passes through the wire, a magnetic field is present inside the solenoid. Solenoids are used in electronic circuits or as electromagnets.

In this lab we will explore factors that affect the magnetic field inside the solenoid and study how the field varies in different parts of the solenoid. By inserting a Magnetic Field Sensor between the coils of the Slinky, you can measure the magnetic field inside the coil. You will also measure 0, the permeability constant. The permeability constant is a fundamental constant of physics.

OBJECTIVES

• Determine the relationship between magnetic field and the current in a solenoid.

• Determine the relationship between magnetic field and the number of turns per meter in a solenoid.

• Study how the field varies inside and outside a solenoid.

• Determine the value of the permeability constant.

Figure 1

MATERIALS

computer meter stick Labquest Mini DC power supply Logger Pro high current probe Magnetic field sensor cardboard spacers Slinky connecting wires Graphical Analysis or graph paper switch

tape and cardboard

INITIAL SETUP

1. Connect the magnetic field sensor to the Labquest unit. Set the switch on the sensor to High.

46

2. Stretch the Slinky until it is about 1 m in length. The distance between the coils should be about 1 cm. Use a non-conducting material (tape, cardboard, etc.) to hold the Slinky at this length.

3. Set up the circuit and equipment as shown in Fig. 1. Wires with clips on the end should be used to connect to the Slinky.

4. Turn on the power supply and adjust it so that when the switch is held closed, the current is as close to 2.0 A as possible. (It is somewhat difficult to get exactly 2.0 A because of the very small resistance of the Slinky.)

Warning: This lab requires fairly large currents to flow through the wires and Slinky. Only close the switch so the current flows when you are taking a measurement. The Slinky, wires, and possibly the power supply may get hot if left on continuously.

5. Open the Logger Pro file "Magnetic field" in the folder Lab 08. A graph will appear on the screen. The vertical axis has magnetic field scaled from –0.3 to +0.3 mT. The horizontal axis has time scaled from 0 to 20 s. The Meter window displays magnetic field in millitesla, mT. The meter is a live display of the magnetic field intensity.

PRELIMINARY QUESTIONS

1. Hold the switch closed. The current should be about 2.0 A. Place the Magnetic Field Sensor between the turns of the Slinky near its center. Rotate the sensor and determine which direction gives the largest magnetic field reading. What direction is the white dot on the sensor pointing?

2. What happens if you rotate the white dot to point the opposite way? What happens if you rotate the white dot so it points perpendicular to the axis of the solenoid?

3. Stick the Magnetic Field Sensor through different locations along the Slinky to explore how the field varies along the length. Always orient the sensor to read the maximum magnetic field at that point along the Slinky. How does the magnetic field inside the solenoid seem to vary along its length?

4. Check the magnetic field intensity just outside the solenoid.

PROCEDURE

Part I How Is The Magnetic Field In A Solenoid Related To The Current?

For the first part of the experiment you will determine the relationship between the magnetic field at the center of a solenoid and the current flowing through the solenoid. As before, leave the current off except when making a measurement.

1. Place the Magnetic Field Sensor between the turns of the Slinky near its center.

2. Close the switch and rotate the sensor so that the white dot points directly down the long axis of the solenoid. This will be the position for all of the magnetic field measurements for the rest of this lab.

47

Figure 2

3. Click to begin data collection. Wait a few seconds and close the switch to turn on the current.

4. If the magnetic field increases when the switch is closed, you are ready to take data. If the field decreases when you close the switch, rotate the Magnetic Field Sensor so that it points the other direction down the solenoid.

5. With the Magnetic Field Sensor in position and the switch open, click the "Set zero point" button  on the toolbar to zero the sensor and remove readings due to the Earth’s magnetic field, any magnetism in the metal of the Slinky, or the table.

6. Adjust the power supply so that roughly 0.5 A of current flows through the coil when the switch is closed.

7. Click to begin data collection. Close the switch for at least 10 seconds during the data collection.

8. View the magnetic field vs. time graph and determine the region of the curve where the current was flowing in the wire. Select this region on the graph by dragging over it. Determine the average magnetic field while the current was on by clicking on the Statistics button, . Record the average magnetic field and the current in the data table.

9. Increase the current by roughly 0.5 A and repeat Steps 7 and 8.

10. Repeat Step 9 up to a maximum of 2.0 A.

11. Count the number of turns of the Slinky and measure its length. If you have any unstretched part of the Slinky at the ends, do not count it for either the turns or the length. Calculate the number of turns per meter of the stretched portion. Record the length, turns, and the number of turns per meter in the data table.

Part II How is the Magnetic Field in a Solenoid Related to the Spacing of the Turns?

For the second part of the experiment, you will determine the relationship between the magnetic field in the center of a coil and the number of turns of wire per meter of the solenoid. You will keep the current constant. Leave the Slinky set up as shown in Figure 1. The sensor will be oriented as it was before, so that it measures the field down the middle of the solenoid. You will be changing the length of the Slinky from 0.5 to 2.0 m to change the number of turns per meter.

12. Adjust the power supply so that the current will be 1.5 A when the switch is closed.

13. With the Magnetic Field Sensor in position, but no current flowing, click  on the toolbar to zero the sensor and remove readings due to the Earth’s magnetic field and any magnetism in

48

the metal of the Slinky. Since the Slinky is made of an iron alloy, it can be magnetized itself. Moving the Slinky around can cause a change in the field, even if no current is flowing. This means you will need to zero the reading each time you move or adjust the Slinky.

14. Click to begin data collection. Close and hold the switch for about 10 seconds during the data collection. As before, leave the switch closed only during actual data collection.

15. View the magnetic field vs. time graph and determine where the current was flowing in the wire. Select this region on the graph by dragging over it. Find the average magnetic field while the current was on by clicking on the Statistics button, . Count the number of turns of the Slinky and measure its length. If you have any unstretched part of the Slinky at the ends, do not count it for either the turns or the length. Record the length of the Slinky and the average magnetic field in the data table.

16. Repeat Steps 13 – 15 after changing the length of the Slinky to 0.5 m, 1.5 m, and 2.0 m. Each time, zero the Magnetic Field Sensor with the current off. Make sure that the current remains at 1.5 A each time you turn it on.

ANALYSIS

1. Plot a graph of magnetic field B vs. the current I through the solenoid. You may launch a fresh copy of LoggerPro, or use the file "magnetic field graph' in the Lab 08 folder.

2. How is magnetic field related to the current through the solenoid?

3. Determine the equation of the best-fit line, including the y-intercept. Note the constants and their units.

4. For each of the measurements of Part II, calculate the number of turns per meter. Enter these values in the data table.

5. Plot a graph of magnetic field B vs. the turns per meter of the solenoid (n). Use either Graphical Analysis or graph paper.

6. How is magnetic field related to the turns/meter of the solenoid?

7. Determine the equation of the best-fit line to your graph. Note the constants and their units

8. From Ampere’s law, it can be shown that the magnetic field B inside a long solenoid is

B nI= 0

where 0 is the permeability constant. Do your results agree with this equation? Explain.

9. The permeability constant for a vacuum, 0, has a value of 410 -7 Tm/A. Assuming the

equation in step 8 applies to the Slinky, obtain a value of  from your graphs, and compare with the 'theoretical' value.

10. Was your Slinky positioned along an east-west, north-south, or on some other axis? Will this have any effect on your readings?

49

DATA TABLES

Part I

Current in solenoid I Magnetic field B (A) (mT)

0.5

1.0

1.5

2.0

Length of solenoid (m)

Number of turns

Turns/m (m –1

)

Part II

Length of solenoid Turns/meter n

CCurrentCC

Magnetic field B

(m) (m –1

) (mT)

Number of turns in Slinky

50

Lab 9. Faraday's Law & Lenz's Law

In 1831, Michael Faraday made a discovery with enormous technological consequences. He

discovered that for an electric current in one circuit to induce a current in a second circuit, the

current in the first circuit must be changing with time. The induced current is caused by the

changing magnetic flux through the area bounded by the second circuit, which in turn is

generated by the changing current in the first circuit. This changing flux induces an emf in the

second circuit and, consequently, an induced current. The technological consequence of all this

is our whole system of electrical power generation. Faraday’s Law summarizes this

quantitatively, stating that the magnitude of the induced emf in a conducting loop is equal to the

rate at which the magnetic flux through the area bounded by the loop is changing with time, i.e.

 t

 −= or, more correctly,  .

dt

d −=

The negative sign is related to a sign convention for the direction of the induced current.

Alternatively, this direction is given by Lenz’s Law, which states that an induced emf or current

tends to oppose, or cancel out, the changing flux that caused it. So if the flux is increasing, the

magnetic field of the induced current will tend to decrease the flux. In this lab, you will be

performing a series of mainly qualitative experiments that will strengthen your understanding of

Faraday’s and Lenz’s Laws. OBJECTIVES

• Change the flux through a circuit by moving a magnet.

• Change the flux through a circuit by changing the current in another circuit.

• Perform a series of steps to test the validity of Lenz's Law. MATERIALS

nested pair of solenoids center-reading galvanometer power supply connecting wires bar magnet current probe computer

compass Labquest Mini

PRELIMINARY QUESTIONS

1. What is the difference between magnetic field and magnetic flux?

2. Consider the magnetic field lines surrounding a disc magnet as pictured at right. The magnet moves from right to left through the wire loop. Describe how the magnetic flux through the surface defined by the loop changes (if at all) as the magnet 1) approaches the loop, 2) passes through the loop, and 3) recedes from the loop. Sketch a graph of magnetic flux through the surface vs. time as the magnet undergoes this motion.

51

PROCEDURE

Part 1 Moving Magnet

1. Connect the terminals of the large solenoid to the terminals of the center reading galvanometer. Push the north end of the bar magnet into the end of the solenoid remote from the terminals, observing the galvanometer during the process. Now hold the magnet steady for several seconds and then pull it out of the coil. Repeat these procedures varying the speed of the magnet.

2. Q1. Does the galvanometer deflect to the left or the right when a) the magnet is being pushed in b) the magnet is being pulled out c) the magnet is being held steady? Q2. How does the maximum deflection of the galvanometer appear to depend on the speed with which the magnet is moved? Why? Q3. How do your observations lend support to the statement: “A steady magnetic field cannot induce currents in a stationary conductor”?

3. Repeat steps 1 and 2, this time pushing the south end of the magnet into the end of the solenoid.

Part 2 Changing Current

4. With the terminals of the larger-diameter solenoid still connected to the galvanometer, connect those of the smaller coil, via a variable resistor, to a power supply as shown in Fig. 1. Switch on the power supply and adjust the output to maximum.

Figure 1

5. The current through the smaller coil creates a magnetic field, as should be observed in the deflection produced on a nearby compass needle. Place the smaller solenoid inside the larger one and stand the coils upright on the bench. Adjust the variable resistor to give minimum current (turn knob counter-clockwise). Then turn the knob rapidly from the minimum to the maximum current setting while observing the galvanometer. Leave it at the maximum current setting for several seconds and then turn it rapidly to the minimum current setting, again while observing the galvanometer.

6. Q4. Does the galvanometer deflect to the left or right while the current in the smaller coil is a) increasing b) decreasing c) not changing? Q5. State, giving reasons, whether the answers given to Q.4. are to be expected on the basis of those given in Q.1.

52

7. Insert the metal rod fully into the smaller solenoid and repeat the operations of increasing, holding steady and decreasing the current in the smaller solenoid. Also try varying the rate with which the current is increased and decreased. (The effect of the rod, which you will observe, is due to a process called “magnetization.” The magnetic field of the current in the inner solenoid causes the magnetic dipole moments of the atoms in the rod to become aligned. The magnetic fields of these dipoles then add to the field of the inner solenoid resulting in a considerably stronger magnetic field and a correspondingly greater flux through each turn of the outer solenoid.)

8. Q6. What is the effect of the presence of the rod on the current induced in the larger solenoid? Q7. How does the induced current depend on the rate at which the current in the smaller solenoid is altered?

9. With the rod still inserted, place a current probe in the circuit between the power supply and the variable resistor. The red connecting wire should be connected to the positive terminal (red) of the power supply. Also connect a tap switch between the negative terminal (black) of the power supply and the smaller solenoid. Open the Logger Pro file "Faraday's Law" in the folder Lab 09 for current measurement and graph plotting, and zero the current probe. With the tap switch closed, adjust the variable resistor to give a current of 150 mA. Observe the maximum galvanometer deflection when the switch is opened and closed. Repeat with currents of 175, 200, and 225 mA. Create a graph of galvanometer deflection vs. current.

10. Q8. What does the graph indicate?

Part 3 Exploration of Lenz's Law

In this section you will explore whether, when a magnet is pushed into a solenoid, the induced current creates a magnetic field that exerts a repulsive force on the magnet, as indicated in Fig. 2. ("Like" poles repel.) To show that this is the case, you must first determine the direction of the induced current, and then, while driving a larger current through the solenoid in the same direction, check the direction of the magnetic field, which should now be large enough to be detected. Figure 2

Figure 3

N S

Direction of motion

NS

N SA

B

Power supply

Right terminal

Left terminal

10,000 

a) b)

53

11. Connect the galvanometer to the larger solenoid and push the north pole of the bar magnet into the end farthest from the terminals as shown in Fig. 3a. Note whether the galvanometer deflects to the right or left. Also note which terminal of the solenoid is connected to which terminal of the galvanometer.

12. Disconnect the solenoid and set up the circuit shown in Fig. 3b. THE 10,000  RESISTOR IS TO PROTECT THE SENSITIVE GALVANOMETER. FAILURE TO INCLUDE IT IN THE CIRCUIT WILL RESULT IN EXPENSIVE DAMAGE. Alter the connections to the galvanometer, if necessary, to obtain the same direction of deflection as in step 11. Reproduce the circuit diagram of Fig. 3b and mark on it the direction of the current. You are now in a position to reproduce Fig. 3a and also mark on it the direction of the (induced) current.

13. Adjust the power supply output to maximum and connect it to the solenoid in such a way that the current passes through the solenoid in the same direction as indicated in your Fig. 3a. You have now created a magnetic field in the same direction as that due to the induced current, but one which is much stronger.

14. Use the compass to determine whether the end of the coil remote from the terminals behaves as a north or south pole. Label the poles on your figure of the coil.

ANALYSIS

1. Are your results consistent with Lenz's Law?

54

Lab 10. Reflection and Refraction

Image formation by reflection and refraction is best understood using a graphical technique

called ray tracing. A ray is line that we draw on a diagram indicating the direction in which light

is traveling. The nearest physical approximation to a light ray is a narrow beam of light like you

get from a laser or, in this lab, from a light source and a narrow slit. When such a beam of light,

strikes a boundary separating two transparent media, for example an air-water interface, it is

partially reflected and partially refracted. See Fig. 1. In this experiment, the laws governing these

processes will be investigated. The law of reflection relates the angles of incidence, a, and

reflection, r. The law of refraction relates the angles of incidence, a, and refraction, b to the refractive indices, na and nb.

Figure 1

OBJECTIVES

• Investigate the formation of a virtual image by a plane mirror and the law of reflection that governs it.

• Investigate refraction at a boundary and the law of refraction (Snell's Law) that governs it

• Investigate the phenomenon of total internal reflection. MATERIALS

ray box rectangular transparent prism plane mirror semicircular transparent prism magnetic pins white board PRELIMINARY QUESTIONS

1. When looking obliquely at a window, you may see two reflected images close to each other. What causes this?

2. Binoculars and periscopes use prisms instead of mirrors to reflect light. How does this happen? Draw a sketch.

3. When hot air rises above a stove top, objects behind it appear to shimmer. What causes this?

4. In Fig.1, which refractive index is greater, na or nb? How would the figure appear if it was the other way round? Draw a sketch.

55

PROCEDURE

PART 1: THE LAW OF REFLECTION

Figure 2

1. Position the mirror near the center of the white board. Outline the rear surface of the mirror with a marker. (That's where the reflective coating is.)

2. Place a magnetic "pin" at a point A approximately 10 cm from the mirror, as shown in Fig. 2. This pin is the object. Rays from A are reflected by the mirror in such a way that they appear to be coming from A', the virtual image of A.

3. Place a second pin B close to the mirror such that a ray traveling from A to B will strike the mirror at about 45o. The corresponding reflected ray may now be found by lining up the images of A and B in the mirror and placing two locating pins C and D so that all four appear to be in line.

4. Mark the position of the pins and draw lines joining AB and CD to meet the mirror as in Fig. 2. Also mark in the normal PN. Measure the angles of incidence and reflection with a protractor, and enter the values in the data table.

5. Repeat steps 3 and 4 for an angle of incidence of roughly 30°.

6 Both reflected rays appear to originate at the same point (the image) behind the mirror. Extend the rays backward to locate A'. Measure the perpendicular distances of A and A' from the mirror and enter the values in the data table as object distance and image distance, respectively.

PART 2: THE LAW OF REFRACTION

7. Adjust the ray box to produce a narrow beam of light. Place a sheet of white paper on the bench with the transparent rectangular block at the center of the paper. Draw the outline of the block on the paper and make a small mark on the paper near the midpoint of one of the long sides.

A

B C

D N

P

~10cm

A'

Mark behind pins

56

Figure 3

8. Direct the light beam towards the mark making the angle of incidence about 30o. Mark two points on the incident ray and two on the emerging ray.

9. Remove the block and trace the path of the ray as in Fig. 3. Note that you will probably not be able to see the ray within the block but can still tell its trajectory by connecting the point where it entered to the point where it left the block. Measure and record the angles of incidence and refraction at the first surface in the data table.

10. Repeat this procedure for five different angles of incidence between 10o and 60o. You may need to change where the ray enters the block.

PART 2: TOTAL INTERNAL REFLECTION

11. Place the semicircular transparent block on a sheet of paper and direct the narrow beam of light from the ray box through the curved surface towards the center of the flat face.

12. Rotate the block about this central point until the angle of refraction at the flat face is 90o, i.e. the emerging refracted ray is skimming the flat surface of the block. Outline the flat surface and mark the position of the incident ray. Remove the block, draw the incident ray and measure the angle of incidence. When the angle of refraction is 90°, the angle of incidence is called the "critical angle."

13. Note what happens to the intensity of the reflected beam if the angle of incidence is larger than the critical angle, and also note whether there is a refracted beam at the flat surface.

ANALYSIS

1. What is the relationship between the angles of incidence and reflection?

2. What is the relationship between the object and image distances for a plane mirror?

3. Plot a graph of sina (y axis) vs. sinb (x axis) and, from the slope, calculate the refractive index of the rectangular block. (The refractive index of air is 1.00029 which you can approximate to 1.0.)

4. Calculate the refractive index of the semicircular block.

5. What happened to the refracted ray when the angle of incidence was larger than the critical angle?

6. What happened to the intensity of the reflected ray when the angle of incidence was larger than the critical angle?

57

DATA TABLES

Angle of incidence Angle of reflection

Object distance (cm) Image distance (cm)

Refractive index of rectangular block _____________ Critical angle for semicircular block _______________ Refractive index of semicircular block______________

Angle of incidence, a Angle of refraction, b sin a sin b

58

Lab 11. Mirrors, Lenses, Telescope Lenses and mirrors are the basic building blocks of such optical instruments as cameras,

binoculars, telescopes, microscopes, magnifying mirrors, movie projectors, etc. In this lab, the

basic properties of lenses and mirrors will be investigated. In the last part of the experiment you

will construct and examine the properties of an astronomical telescope. Throughout the lab, you

will be using the lens/mirror formula:

s s' f

+ = 1 1 1

................................(1)

where f, is the focal length of the mirror or lens, s is the distance from the object to the lens or

mirror (object distance), and s' is the distance from the lens or mirror to the image (image

distance). The magnification, M, of an image created by a lens or mirror is given by

h' s'

M h s

  = = − 

  ...........................(2)

where h and h’ are the object and image heights, respectively.

OBJECTIVES

• Measure the focal lengths of mirrors and lenses.

• Clarify what is the difference between real and virtual objects and images.

• Construct an astronomical telescope and measure its magnification. MATERIALS

light box optical bench mirror and lenses screen PRELIMINARY QUESTIONS

1. Is the image projected on a movie screen real or virtual? What about the image of yourself seen in a bathroom mirror?

2. Hold a shiny spoon in front of you. What differences do you notice about the image of your face seen in the convex and concave sides?

3. Where are the images formed by each side of the spoon? In front or behind the spoon? (Try the parallax method. Look at the image of an overhead light. Hold the tip of a pencil where you think the image is. Move your head from side to side. If the image and pencil tip appear to move relative to each other, adjust the position of the pencil back and forth until they appear to move as one.)

PART 1: CONCAVE MIRROR

CAUTION: In order to remove, install or change the position of any of the lens/mirror holders, gently squeeze the plastic tab on the side of the holder and then slide the holder along the optical bench. Do not lift the holder straight up to remove or push straight down to install.

59

1. The “object” for this part of the lab is an illuminated crossed arrow on the front of a light box. Set up the concave mirror so that it reflects back onto the half-screen which should be placed as close to the object as possible, as shown in Fig. 1.

Figure 1

2. Now adjust the position of the concave mirror until a clear, sharp image is obtained on the screen. The object and image distances are then equal to one another (s = s’), and also equal to the radius of curvature, r, of the mirror. Measure the distance and draw a ray diagram showing why this is the case. Enter the value of r in the data table. How big is the image compared with the object? Enter the magnification in the data table.

Figure 2

3. Reflect the light from a distant object (s  ), such as a building or tree seen through a window, onto the screen as shown in Fig. 2. Adjust the mirror-screen distance until you get a sharply focused image.

4. Measure the distance between the mirror and the screen when the image is in sharp focus. This is the focal length, f, of the mirror. Enter the value in the data table

PART 2: CONVERGING LENS

5. Mount the lens/lens holder labeled A on the optical bench at a distance of approximately 20 cm from the illuminated crossed arrow on the light box. Mount the screen on the opposite side of the lens.

6. Move a screen back and forth until a sharp image is formed. Measure the object and image distances.

7. Repeat for 4 more different object distances.

60

8. Focus light from a distant object onto the screen, as you did for the concave mirror. Measure the distance from lens to screen. This is the focal length, f, of the lens. Record the value in the data table.

PART 3: DIVERGING LENS

Figure 3

In Fig. 3, converging lens A (the one you used in Part 2) by itself would produce a real image at the point of convergence of the refracted rays. If diverging lens C is interposed between lens A and this real image, a new real image will be formed as shown. The original real image formed by lens A becomes a virtual object for lens C. According to the sign convention, the corresponding object distance for lens C will be negative.

9. Reproduce the set-up in Fig. 3 but without lens C. Adjust the position of the converging lens A to give a real image on a screen with a relatively short image distance, less than 20 cm. Measure this image distance.

10. Next, insert the diverging lens between lens A and the screen, and reposition the screen until the image is in sharp focus.

11. Measure the new-image distance from lens C. Note that |s| in this case is the distance from lens C to where the image was formed by lens A alone.

PART 4: THE TELESCOPE

The final part of the experiment is to construct a simple telescope. You will use the converging

lens from the previous section as the eyepiece (lens A) and a second converging lens with a

longer focal length for the objective (lens B). The setup is shown in Fig. 4 with the equation for

the angular magnification given by:

angular magnification = obj

eye

f

f

Lens A

Lens C

Real image for lens A, virtual object for lens C

Real image for lens C

|s|

s'

Real object for lens A

61

Figure 4

12. Repeat step 8 for lens B to obtain its focal length.

13. Mount lens A and B at a distance apart equal to the sum of their focal lengths.

14. If you look through lens A at a distant object, so that lens B is between the object and lens A, you should see an enlarged, inverted image, though you may need to slide lens A back and forth to obtain a well-focused image.

15. In the lab there is a large graded scale on one wall. Take your telescope to the other end of the lab from the scale and look at the scale through your telescope with one eye. With the other eye, look at the scale directly. Estimate how many divisions of the scale seen through the telescope correspond to the entire ten divisions of the scale as seen with the unaided eye.

ANALYSIS

1. When the object and image distances for the mirror are equal, what is the theoretical magnification? How does this compare with the value you entered in the data table?

2. What is the relationship between f and r for the mirror?

3. For the converging lens, plot a graph of 1/s (x axis) vs. 1/s' (y axis).

4. If you rearrange equation 1 as s' s f

= − + 1 1 1

, it has the form y mx a= + . Record the slope and

intercept of your graph in the data table. From the intercept, obtain the focal length.

5. How did the focal length obtained from the intercept compare with that obtained from the

distant object?

6. Lens A had a real object whereas lens C had a virtual object. What do you notice is the difference between the incident rays approaching each lens?

7. Lens A had a real image whereas the image in Fig. 2 of last week's lab (Reflection and Refraction) was virtual. What do you notice is the difference between the rays leaving lens A and those leaving the plane mirror in that figure?

8. How did the measured angular magnification of the telescope compare with the theoretical prediction?

Objective lens B

fobj feye

Eyepiece lens A

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DATA TABLES

Slope of graph = _____________ Intercept of graph = ___________ Focal length from intercept = ___________ cm Focal length from distant object = ___________ cm

Table 1 Mirror

Radius of curvature of mirror = cm Focal length of mirror = cm

Magnification =

Table 2 Converging Lens

Object distance, s (cm) Image distance, s' (cm) 1/s (cm)-1 1/s' (cm)-1

Table 3 Diverging Lens

Image distance for lens A = cm Object distance for lens C = cm

Image distance for lens C = cm Focal length of lens C = cm

Table 4 Telescope

Focal length of lens A = cm Focal length for lens B = cm

Theoretical angular magnification = Measured magnification =

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Lab 12. Double-Slit Interference

Until the beginning of the 19th century, the question of whether light propagated as a type of

wave, or as a beam of particles had not been answered. Newton favored the particle theory to

explain why light appeared to travel in straight lines, whereas Robert Hooke and Christian

Huygens were able to explain refraction by assuming that light traveled as a wave with different

speeds in different media. Then in 1801, Thomas Young performed his crucial two-slit

interference experiment, which clearly demonstrated the wave nature of light.

..........................(1)

Figure 1

In Young’s experiment, light waves of wavelength  spread out from each slit by a process

called diffraction as shown in Fig. 1. Along the directions where the crests reinforce each other,

as indicated by the solid lines, the wave intensity is high. Along the directions where a crest is

cancelled by a trough, as indicated by the dashed lines, the intensity is low. If a screen is

positioned to intercept the waves, an interference pattern of bright and dark "fringes" is obtained.

The condition for maximum brightness at a point on the screen is that the distances from the slits

to that point differ by a whole number of wavelengths, m, where m is an integer. The distance

y between the centers of two adjacent bright fringes is given by equation 1 in Fig. 1.

OBJECTIVES

In this experiment, you will

• Compare the patterns of light produced by a single slit and by two slits side-by-side.

• Investigate how the spacing between adjacent fringes depends on the spacing between two slits, and on the wavelength of light being used.

• Determine the wavelength of light from the two-slit pattern and compare it with the wavelength of the laser light source.

MATERIALS

green and red lasers optical bench single slit set double slit set

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PRELIMINARY QUESTIONS

1. What does the acronym LASER stand for? What characteristic of a laser makes it suitable for today's experiment?

2. What is meant by constructive and destructive interference?

3. Why do you see colors when you look at reflected light from a CD or DVD disk, or when you look at a soap bubble or oil film on water?.

4. What do you think causes the colors on the artwork panels on the side of HLS2 (Health Sciences building) which change with time of day and the angle from which you view them?

PROCEDURE

CAUTION: In performing this experiment, you will be using lasers that produce narrow, low

divergence beams of highly monochromatic light. The beams are of high intensity and eye

damage could result from looking directly into the laser. Beware of accidentally directing the

beam into your own or other people’s eyes either directly or by reflection from a shiny object.

CAUTION In order to remove, install or change the position of any of the optical components,

gently squeeze the plastic tab on the side of the component and then slide it along the optical

bench. Do not lift it straight up to remove or push straight down to install.

1. Mount the shorter wavelength laser (wavelengths are printed on the back) at one end of the optical bench and the white screen at the other end. In between, and close to the laser, mount the single slit accessory. Adjust the distance between the slit and screen to a convenient value.

2. Switch on the laser, and carefully adjust the single slit accessory until the laser beam is incident on the variable slit. (Note that the slit width varies from 0.02 to 0.2 mm.) This will generally require rotating the single slit disk as well as the rotatable part of the holder. Make final adjustments to produce a bright pattern on the screen using a slit width at about 50% of the available range.

3. The part of the slit in the laser beam should be vertical. Note in which direction the light spreads out on the screen.

4. The "single slit diffraction pattern" is due to constructive and destructive interference between light waves originating from different points across the width of the slit. Sketch a graph of the perceived intensity vs. horizontal distance across the pattern. Be careful to note the width of the central bright maximum compared with those of the subsidiary maxima on either side.

5. Holding the rotatable part of the holder steady, rotate the slit disk in order to vary the width of the slit. Note the appearance of the pattern for the narrowest and widest slit settings.

6. Switch off the laser and replace the single slit accessory with the multiple slit accessory, having first noted the positions of double slits of width 0.04 mm and with slit separations of 0.125, 0.25, 0.5, and 0.75 mm. The last one, 0.75 mm, can be obtained using the widest separation on the variable double slit. Again adjust the position of the accessory so that the slits-to-screen distance is the same as in step 1. Record the value on the data table page.

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7. Switch on the laser and make adjustments so that the beam is incident on the double slits with separation 0.125 mm. Observe that the interference pattern looks like the single slit pattern, but with smaller superimposed interference fringes. These are due to interference between waves coming from each slit.

8. Measure the average distance between adjacent bright fringes. To do so, tape a piece of white paper on the screen. Mark the position of a two bright fringes about 5 cm to the left and right of the center, then count the number of spaces between them. By division you can obtain the average distance, y, between adjacent fringes. Enter the value in the data table.

9. Repeat Step 8 for slit separations of 0.25, 0.5, and 0.75 mm.

10. Replace the green laser with the red one. For just one set of double slits (your choice), obtain the average fringe spacing and enter it in the data table together with the slits-to-screen distance, and the slit separation.

EVALUATION OF DATA

1. With the slit vertical, in which direction does the light spread out by diffraction?

2. Describe the appearance of the single slit diffraction pattern for a narrow slit and for a wider slit.

3. For the double slits, what happens to the interference fringes as the slit separation is increased? Is this consistent with equation 1?

3. For the double slit experiment, plot a graph of the average fringe separation, y, (y axis) vs. the reciprocal of the slit separation, 1/d, (x axis).

4. Obtain the slope of the graph and, together with the slits-to-screen distance, L, calculate the wavelength of the laser. Enter the value in the data table together with the value printed on the laser. What is the percentage difference between the values?

5. Calculate the wavelength of the red laser from the fringe separation, etc., and compare with the value printed on the laser by calculating the percentage difference.

6. What is the effect of wavelength on the fringe separation? Is this consistent with equation 1?

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DATA TABLES

Slits to screen distance, L = _____________cm Calculated wavelength of green laser = ___________nm Wavelength printed on laser = ___________ nm Percentage difference = ___________ %

Slits to screen distance, L = _____________cm Calculated wavelength of red laser = ___________nm Wavelength printed on laser = ___________ nm Percentage difference = ___________ %

Double slit with green laser

Slit separation, d (cm) 1/d (cm)-1 Fringe separation, y, (cm)

Slit separation, d (cm) Fringe separation, y, (cm)