physics 204 laboratory guidephysics.wooster.edu/lindner/ph204spring2011/ph204lab.pdf1.6 formal...

Wing-Chi Poon

Physics 204

Laboratory Guide

Physics DepartmentThe College of Wooster

2011 May 13

Contents

1 Coulomb Experiment 91.1 Two Kinds of Charge . . . . . . . . . . . . . . . . . . . . . . . . . 91.2 Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3 Charging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4 Force vs. Separation . . . . . . . . . . . . . . . . . . . . . . . . . 111.5 Force vs. Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.6 Formal Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Ampere Experiment 132.1 Apparatus Preparation . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Fine Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 Caution! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4 The Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.5 Force vs. Current . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.6 Force vs. Distance . . . . . . . . . . . . . . . . . . . . . . . . . . 172.7 Formal Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 Faraday Experiment 193.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3 DataStudio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.4 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.5 Formal Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4 Ray Optics Experiments 234.1 Propagation [Optional] . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3 Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.4 Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.5 Total Internal Reflection . . . . . . . . . . . . . . . . . . . . . . . 28

5 Wave Optics Experiments 295.1 Single Slit Diffraction . . . . . . . . . . . . . . . . . . . . . . . . 295.2 Double Slit Interference . . . . . . . . . . . . . . . . . . . . . . . 30

3

4 CONTENTS

5.3 Diffraction Grating . . . . . . . . . . . . . . . . . . . . . . . . . . 315.4 Hair Strand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

6 Simple Circuit Experiments 356.1 Configuring the Voltage Source . . . . . . . . . . . . . . . . . . . 356.2 Using a Multimeter . . . . . . . . . . . . . . . . . . . . . . . . . . 366.3 Current Flow in a Circuit . . . . . . . . . . . . . . . . . . . . . . 366.4 Series and Parallel Resistors . . . . . . . . . . . . . . . . . . . . . 376.5 More Complex Resistors . . . . . . . . . . . . . . . . . . . . . . . 38

7 Ohm Experiment 417.1 Ohmic Resistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417.2 Light Bulb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417.3 Diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Appendices

A Formal Report Guide 43

B Electromagnetic Units 49

C Resistor Units 51

List of Tables

A-1 Electromagnetic Units . . . . . . . . . . . . . . . . . . . . . . . . 49

A-1 Resistor codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5

6 LIST OF TABLES

List of Figures

1.1 Coulomb apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1 Ampere apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.1 Faraday apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.1 Propagation tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Ray tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3 Reflection tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.4 Measuring angles . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.5 Refraction tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.6 Dispersion tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.1 Single slit interference . . . . . . . . . . . . . . . . . . . . . . . . 305.2 Double slit interference . . . . . . . . . . . . . . . . . . . . . . . . 315.3 Grating interference . . . . . . . . . . . . . . . . . . . . . . . . . 32

6.1 Using a multimeter . . . . . . . . . . . . . . . . . . . . . . . . . . 366.2 Simple circuit A . . . . . . . . . . . . . . . . . . . . . . . . . . . 376.3 Simple circuits BC . . . . . . . . . . . . . . . . . . . . . . . . . . 386.4 Simple circuits D . . . . . . . . . . . . . . . . . . . . . . . . . . . 396.5 Simple circuits E . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

7.1 Diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

7

8 LIST OF FIGURES

Chapter 1

Coulomb Experiment

Augustin de Coulomb conducted the first recorded quantitative investigation [1]of the electrical force in 1784. Coulomb used a very sensitive torsion balance tomeasure the forces between two “point charges”, charged bodies whose dimen-sions are small compared to the distance between them. Consequently, the SIunit of charge is named for him.

Coulomb found that the force grows weaker as the distance between thecharges increases, and that it also depends on the amount of charge on eachbody. More specifically, the force of attraction or repulsion between two pointcharges is directly proportional to the product of the charges and inversely pro-portional to the square of the distance between them. The direction of the forceon each particle is always along the line joining the two particles; pulling themtogether when the two charges are opposite, and pushing them apart when thecharges are the same. Mathematically, the vector electric force on a stationarypoint charge q separated by the vector displacement ~r from a stationary chargeQ is

ε0 ~FE = qQ

4πr2r, (1.1)

or~FE = k

qQ

r2r, (1.2)

where r is the magnitude of the separation and r = ~r/r is its direction.In this experiment, measure the force between electrical charges by balancing

electrical repulsion with gravitational attraction. Suspend a small charged ballwith an insulating thread and measure the deflection of the suspended ballfrom vertical as a second charged ball is brought near. Thereby determine theelectrical force from the ball’s weight and deflection.

1.1 Two Kinds of Charge

Coulomb’s law of electricity is reminiscent of Newton’s law of gravity, except theelectric force can be attractive or repulsive while the gravitational force is only

9

10 CHAPTER 1. COULOMB EXPERIMENT

attractive. The source of the difference is the existence of two kinds of electricalcharge, conventionally called “positive” and “negative” because they combinelike positive and negative numbers. Demonstrate the two kinds of electricalinteraction using Scotch tape strips. Place two 10-cm strips of Scotch tape onthe lab table with the sticky sides down. Curl over one end of each tape to makea non-stick handle. Quickly peel the tapes off the table and bring the non-stickysides toward each other. What happens?

Place two strips of tape on the table sticky side down and label them Bfor bottom. Press another tape on top of each of the B pieces, and label thesestrips T for top. Quickly peel each pair of strips off the table, and then pull thetop and bottom strips apart. Describe all the pairwise interactions between thetapes (TT, TB, BT, BB). What do you conclude?

1.2 Preparation

Lower a ball into the center of the chamber (if it is not already there). Pull themonofilament through the precut slits at the top of the chamber. These slits arecentered on the top edge of the front and back faces of the chamber. Once themonofilament has been pulled into the slit, the height and position of the ballcan be adjusted by pulling on the free ends of the monofilament. The suspendedball’s final position should be the same height as the ball mounted on the guideblock and should be centered (front to back) in the chamber. Cover the topof the chamber with either the clear or hardboard top to help eliminate theeffects of air currents and breezes. A mirror fastened to the back surface of thechamber helps to eliminate measurement errors due to parallax. When makingmeasurements, always make sure the ball’s image in the mirror is completelycovered by the ball itself. This insures consistent measurements.

1.3 Charging

Begin by inductively charging the sphere fastened to the guide block. This maybe done by vigorously rubbing a strip of vinyl with a bit of felt, then holdingthe resulting charged vinyl strip close to (but not touching) the small graphitecoated sphere. Place a finger from your other hand onto the ball, therebygrounding it to allow electrons to flow. Remove your finger and then removethe charged vinyl strip. The sphere on your guide block should now be charged.

From now on work quickly but carefully. If the air is humid, the chargedplaced on the coated spheres will eventually “leak off”. This takes some timeto happen but you should be aware of this fact and work accordingly. In highhumidity, try using a hair dryer to dry the apparatus and the surroundings.If you touch the charged ball with anything at this point, it will immediatelydischarge, and you will need to charge it inductively again.

Insert the charged ball into the chamber through one of the holes in thebase. Gently slide the charged ball up to the suspended ball and bring them

1.4. FORCE VS. SEPARATION 11

α

r

d

QQ m

Fg

Ft

FE

Figure 1.1: Geometry for the Coulomb experiment.

into contact. When they touch, the charge will be equally distributed betweenthe two balls. Each ball will have the same amount of charge. What happensjust before the balls touch? Did they attract or repel or do nothing? What isa possible explanation for this behavior? After the initial attraction and theballs’ touch, what do you observe? Explain what is happening.

1.4 Force vs. Separation

Figure 1.1 shows a force diagram for the two balls. Construct a complete deriva-tion of the force relation

kQ2

r2= FE ∼ mg

d

`, (1.3)

assuming the angle α 1. For constant charge Q, this implies

1

r2∝ d. (1.4)

For a given charging, change r and measure the corresponding d. Obtain atleast six data points. Be sure you have enough data points at large r. (Youmay want to move the sphere attached to the guide block in 0.5 cm steps orsmaller).

Since Eq. 1.4 predicts d ∝ 1/r2, in Igor Pro plot displacement d as afunction of the separation r and try a quadratic fit. Better yet, plot d as afunction of 1/r2 and try a proportional fit. If your data looks linear but does notpoint towards the origin, try a linear fit instead, but then check for systematicerrors. If you graph log d as a function of log r and try a linear fit, the slope ofthe line will be the power dependence of d on r. What do you conclude about

12 CHAPTER 1. COULOMB EXPERIMENT

the relationship between force and separation? Include a copy of your graphswith all the fits in your lab notebook.

It may be necessary to charge the two balls several times initially to get asufficient repulsive force. To do this, repeatedly charge the ball on the guideblock by induction, and then bring it into contact with the suspended ball.Alternately, harvest charge from the Van de Graaff generator. The morecharge you put on the suspended ball, the farther it will it will initially deflect.It may take a little practice to get the right amount of charge for your situation.Remember, the greater the charge, the greater the displacement, and the betterthe resolution of your measurements.

1.5 Force vs. Charge

Systematically halving the charge Qn = Q/2n on one of the balls by touchingit to a third uncharged ball implies

kQQ/2n

r2n∼ mgdn

`, (1.5)

or1

2nr2n∝ dn, (1.6)

where the trial number n = 0, 1, 2, . . .. In this way, obtain at least three datapoints. Once again, first practice and then work quickly. You’ll need as muchinitial charge as possible, so consider harvesting charge from the Van de Graaffaccumulator.

Since Eq. 1.6 predicts dn ∝ 1/(2nr2n), in Igor Pro plot dn as a functionof 1/(2nr2n) and try a proportional fit. If your data looks linear but does notpoint towards the origin, try a linear fit instead, but then check for systematicerrors. What do you conclude about the relationship between force and charge?Include a copy of your graphs with all the fits in your lab notebook.

1.6 Formal Report

Describe your experiment in a formal scientific report using the Appendix Aguidelines. Email yourself electronic copies of all your graphs so you can importthem into a word processing document. Use the scientific graphing programIgor Pro, which automatically calculates uncertainties to all fit coefficients.Use some kind of equation editor to professionally compose the equations inyour report. Consult your instructor for assistance.

Chapter 2

Ampere Experiment

Andre-Marie Ampere first systematically investigated [2] the magnetic forcesassociated with current-carrying wires in 1820. Consequently, the SI unit ofcurrent is named for him.

Coulomb’s Law describes the force between two stationary charges. How-ever, when charges move, Coulomb’s Law is no longer sufficient. A new typeof force arises, the magnetic force. Ampere found that the force decreases asthe distance between the currents increases, and that it decreases as the cur-rents decreases. More specifically, the force of attraction or repulsion betweentwo lines of moving charges (current-carrying wires) is directly proportional tothe product of the currents and inversely proportional to the distance betweenthem. While like charges repel and unlike charges attract, parallel currentsattract and antiparallel currents repel. Also, while the electric force decreasesinversely as the square of the distance, reflecting the spherical symmetry of apoint charge, the magnetic force decreases inversely as the distance, reflectingthe cylindrical symmetry of a wire. Mathematically, the vector magnetic forceper unit length on a stationary current i separated by a perpendicular distances from a stationary current I is

~FB`

= −µ0iI

2πss. (2.1)

In this experiment, measure the magnetic force by balancing it against grav-ity. While a current balance like the one featured here can be used to definethe SI unit ampere, for historical reasons, the Eq. 2.1 force law is not called“Ampere’s Law”; while the former relates current to magnetic force, the latterrelates current to magnetic field.

2.1 Apparatus Preparation

The apparatus should already be assembled, as in Fig. 2.1, but if you need toadjust the balance of the loop, this preparation information may be useful.

13

14 CHAPTER 2. AMPERE EXPERIMENT

Insert the longest aluminum loop through the Fahnstock clips on the pivotedbalance beam. Allow the ends of the loop to protrude approximately 1.0 cmabove the clips. Push the end of the pointer through the center hole of thebalance beam. The threaded end of the pointer should extend 6.5 cm from thebalance beam. Now tighten the set screw on the pivot bar. Insert the shortvertical rod into its hole on the top center of the pivot bar. Slip a Fahnstockclip all the way onto the vertical rod.

Position the pivot bar assembly on the balance frame plates so that thepointer extends toward you. Adjust the cylindrical counterweight so that thepointer comes to rest in a horizontal position. Repeat this step with the sensitiv-ity clip moved near the tip of the vertical rod. Position the pivot bar assemblyso that the long straight section of the wire loop comes to rest parallel to andvery close to the fixed coil of wire. The fixed coil mounted on the frame of thebalance consists of two coils; one is a single turn, and the other is a ten turncoil. The center binding post is common to both coils. The left binding post isconnected to the ten turn coil. The right binding post is connected to the singleturn coil.

FBFBI = Nii

Balanced Loop

s

Figure 2.1: Cross section of the Ampere experiment.

2.2 Fine Tuning

The current balance measures the force on a horizontal rod suspended so thatit is free to move at right angles to its length. You can study the forces exertedby a magnetic field on a current by bringing a magnet up to this rod while thereis a current in it. A force on this current carrying rod causes it to swing awayfrom its original position.

Before running any experiments, the balance must be assembled and ad-justed for maximum sensitivity. The non-magnetic metal rod bent into a U-

2.3. CAUTION! 15

shape is referred to as the balanced loop. The balanced loop should be clippedto the pivoted horizontal bar.

Adjust the balanced loop so that the horizontal part of the loop hangs levelwith the bundle of wires (the fixed coil) on the pegboard frame. Adjust thebalance on the frame so that the loop and coil are parallel as you look down atthem. Make sure the loop swings freely.

Adjust the counterweight cylinder to balance the system so that the longpointer arm is approximately horizontal. Mount the U-shaped zero indicator ina clamp and position the plate so that the zero line is opposite the horizontalpointer.

Set the balance for maximum sensitivity by moving the sensitivity clip upthe vertical rod on the pivot bar until the loop slowly swings back and forth.These oscillations may take as much as 4 or 5 seconds per swing. If the clipis raised too far, the balance may become unstable and tip to one side or theother without righting itself.

2.3 Caution!

This experiment involves high current (although at low voltage). Proceedcautiously and carefully and remember the “one hand in pocket” rule. (Thatis, adjusting the apparatus with two hands might inadvertently allow currentto pass through your body.)

2.4 The Circuit

Make sure that the pivots (pointed contacts) are clean and shiny, and remainthat way throughout the experiment. (You can clean them using the fine gradesandpaper.) The 8 V/6 A HP power supply should drive current through thebalanced loop and then through the fixed coil. (That is, the power supply, thebalanced loop and the fixed coil should all be in series.) Set the power supplyfor minimum output, then turn it on. When you are confident that everythingis operating correctly, slowly increase the current to about 5 A. Bring a smallmagnet close to the balanced current loop. What happens? The magnet is amagnetic dipole. What is the axis of the dipole? What orientation of the magnetproduces the greatest deflection of the current loop?

Check to see which way the pointer rod on the balance swings when youturn on the current. You would like the pointer to swing up. If it doesn’t swingup, what do you have to change in your setup? When changing the wiring inyour circuit, always note the direction of the current in each of the loop and thecoil. Do currents flowing in the same direction attract or repel each other?

If the swing of the pointer rod on the balance is too small or too large, tryusing the other fixed loop. (One fixed loop has 10 turns, and the other has onlyone turn.)


Make weights from some thin wire cut to lengths 1 cm, 2 cm, 5 cm, and 10cm, by bending them into small “S” shaped hooks. Hang them from the notchon the pointer or from each other. The distance from the axis of the balance tothe notch on the pointer is the same as the distance from the axis of the balanceto the bottom of the loop. Therefore, when there is a force on the horizontalsection of the balanced current loop, this will equal the total weight hanging onthe pointer at the notch.

2.5 Force vs. Current

Fix the distance between wires and systematically vary the current throughthem. In this case, Eq. 2.1 implies

W = FB = µ0iI

2πs` = µ0

Ni2

2πs` (2.2)

or

W ∝ i2, (2.3)

where W is the suspended weight that balances the magnetic force, and N = 10,the number of turns in the fixed copper coil.

Carefully level and zero the current balance. Separate the two coils by about0.5 cm. If the coils are too close, the fixed coil no longer looks like aline of current; if they are too far, the magnetic forces are too weakto observe. Operate the HP power supply in the “Constant Current” (CC)mode, so that as you rotate the current knob the voltage will adjust to providethe energy per charge necessary to supply that current.

Begin with a relatively small current (∼ 3 A) and observe the pointer deflect.Hang weights on the end of the pointer to bring the pointer back to the zeromark. Record the current and the amount of weight added to the pointer arm.The added weight is a measure of the force between the wires. Increase thecurrent in small steps (∼ 0.2 A). Balance the pointer again by adding moreweights. Record the current and the total weight. Continue to increase thecurrent in the fixed coil until you reach 5 or 6 A. Alternately, successively addweights and increase the current to balance the pointer.

Since Eq. 2.3 predicts W ∝ i2, in Igor Pro, plot the weight W (in arbitraryunits) as a function of the current i, and try a quadratic fit. Better yet, plot thesuspended weight W against the square of the current i2 and try a proportionalfit. If your data looks linear but does not point towards the origin, try a linearfit instead, but then check for systematic errors. If you plot logW as a functionof log i and try a linear fit, the slope of the line will be the power dependenceof W on i. What do you conclude about the relationship between force andcurrent? Include a copy of your graphs with all the fits in your lab notebook.

2.6. FORCE VS. DISTANCE 17

2.6 Force vs. Distance

Fx the current through the wires and systematically vary the distance betweenthem. In this case, Eq. 2.2 implies

W ∝ 1

s. (2.4)

Carefully level and zero the current balance. Again, operate the HP powersupply in the CC (constant current) mode.

Add a relatively large current (∼ 5 A). Hang weights at the notch in thepointer arm until the pointer is again at the zero position. Record the weightand the separation between wires. Turn off the power supply and move thebalanced loop closer (or farther) from the fixed loop. Repeat this procedureusing 4 or 5 different separations (every few millimeters). Make sure that thebalanced loop and the fixed coil are parallel and that the needle is at the zeroposition during each measurement.

Since Eq. 2.4 predicts W ∝ 1/s, in Igor Pro, plot the suspended weightW (in arbitrary units) as a function of the reciprocal of the separation 1/s andtry a proportional fit. If your data looks linear but does not point towards theorigin, try a linear fit instead, but then check for systematic errors. What doyou conclude about the relationship between force and distance? Include a copyof your graphs with all the fits in your lab notebook.

2.7 Formal Report


Chapter 3

Faraday Experiment

By 1831, Michael Faraday discovered [3] that moving a magnet through a coilof wire induced a current in the wire. Because of his many contributions toelectromagnetism, the SI unit of capacitance is named for him.

Faraday’s law relates a changing magnetic flux to a circulating electric field.More specifically, the electric circulation around a closed loop is equal to minusthe rate of change with time of the magnetic flux through any area bounded bythe loop. The minus sign ensures energy conservation and is sometimes referredto as Lenz’s rule. Mathematically, if a loop ` bounds an area a, then∮

l

~E · d~= − d

dt

∫∫a

~B · d~a, (3.1)

or more succinctlyΓE = −ΦB, (3.2)

where the over-dot is Newton’s notation for time derivative.In this experiment, vertically pass a magnet through a wire coil and measure

the induced electric current. Construct an Atwood’s machine to neutralize theacceleration of the magnet.

3.1 Theory

A bar magnet with a conventional north and south pole is a magnetic dipole.Model it by two magnetic monopoles ±QB a distance d apart. A magneticmonopole moving at a nonrelativistic speed v c has a radial magnetic field

~B ≈ µ0QB

4πr 2r (3.3)

and a circulating electric field

~E ≈ −~v × ~B ≈ −~v × µ0QB

4πr 2r , (3.4)

19

20 CHAPTER 3. FARADAY EXPERIMENT

which produces in a loop of radius r at a distance z the the electric circulation

ΓE =

∮`

~E · d~= µ0QB2

vr2

(z2 + r2)3/2. (3.5)

If the loop is a copper wire of resistance R, the moving monopole’s circulatingelectric field will induce a proportional circulating current

I =1

RΓE = − 1

R ΦB = µ0QB2R

vr2

(z2 + r2)3/2. (3.6)

Hence, if a bar magnet passes through a loop of copper wire, its circulatingelectric field will induce a circulating current

I = µ0vr2QB

2R

(1

((z + d/2)2 + r2)3/2− 1

((z − d/2)2 + r2)3/2

), (3.7)

and the current will first swirl one way and then swirl the other way. In bothcases, the peak currents are proportional to the speed.

3.2 Apparatus

Balance the magnet with a counterweight over a pulley in an Atwood’s machine,as in Fig. 3.1. Since the net force on the bar magnet, it should move verticallywith zero acceleration and constant velocity.

N

S

magnetcounterweight

string

pulley

wirecoil

Figure 3.1: Perspective schematic of the Faraday experiment.

3.3 DataStudio

Turn on the power to the Signal Interface box attached to your computer. Verifythat the Smart Pulley is plugged into digital channel 1 of the interface and thatthe red and black leads attached across the current coil on the RLC circuit boardare plugged into the ± output jacks of the interface box. Launch DataStudio.Click on the digital channel 1 icon and select Smart Pulley.

3.4. PROCEDURE 21

Click on the ± output jacks icon. Select the “Signal Generator” menu itemand increase the sampling rate to 500 Hz. Use the signal generator only to mea-sure the current, not to provide a voltage. Verify that the Signal Generator isoff (not on auto). Check the “Measure Output Current” button; uncheck the“Measure Output Voltage” button.

Drag the “Velocity, Ch 1 (m/s)” down to the graph icon. Add a PowerAmplifier graph to the Velocity graph window by dragging “Output Current(A)” to the center of the velocity graph window. If necessary, double-click onthe graph to invoke the Graph Settings window, select the Layout tab, andselect “One Graph: Multiple Y Scales”.

3.4 Procedure

Move the cylindrical magnet suspended from the Smart Pulley smoothly throughthe coil several times at different average velocities while recording both the coilcurrent and the magnet’s velocity. Practice so the magnet doesn’t strike thesides of the coil.

Since Eq. 3.7 predicts peak current proportional to speed, I ∝ v, use theDataStudio xy-cursor to record the magnet speeds at the minimum and max-imum coil currents. In Igor Pro, plot Imax as a function of v and try a pro-portional fit. Separately plot Imin as a function of v and try a proportional fit.Can you combine all this data into one plot?

Next export the current I as function time t for one run as a text file. Openthis file, delete the two header rows, copy and past the data into Igor Pro, andre-plot it there. Under “Analysis → Curve Fitting...”, select the “Function andData” tab and create a “New Fit Function...” in Igor Pro’s syntax

f(t) = f0 + a ∗ ( 1/( (v ∗ (t− t0) + d/2 )ˆ2 + rˆ2 )ˆ(3/2)

−1/( (v ∗ (t− t0)− d/2 )ˆ2 + rˆ2 )ˆ(3/2) ) (3.8)

based on the Eq. 3.7 current, where t0 is the time the magnet’s center is atthe coil’s center (and the current momentarily vanishes), and f0 is a possibleDC offset in your apparatus. Select the “Coefficients” tab and make reasonableinitial guesses for the five parameters; for example, a = −7.9× 10−6, d = 0.05,and r = 0.045, v = 0.53, t0 = 4.36, f0 = 0.0. Your best guesses will likelybe different; in particular, the sign of the overall amplitude a depends onwhether the north pole of the magnet goes through the coil first or second. Tryto hold r, v, t0, f0 fixed at values you can measure, so a two-parameter fitdetermines the model parameters a ∝ QB and d with the smallest uncertainty.If you have time, repeat for a second run at a different average speed. Includea copy of your graph and all your fits in your lab notebook.

22 CHAPTER 3. FARADAY EXPERIMENT

3.5 Formal Report


Chapter 4

Ray Optics Experiments

Ray optics or geometric optics is the study of light in situations where itswavelength is negligible. In these experiments, test the laws of reflection andrefraction, including the phenomena of dispersion and total internal reflection.

4.1 Propagation [Optional]

How does light travel in air? What determines the shape of a beam of light orthe path a beam of light will take? It partly depends on the the source of thelight.

Slit Plate

Ray Table

Figure 4.1: Optics bench configures for propagation tests.

Configure the equipment as shown in Fig. 4.1 and turn on the light source.Observe the light rays on the Ray Table. Vary the distance of the Slit Platefrom the source. Try rotating the Slit Plate so the slits are horizontal. (Rotateso the plate stays in the same plane; don’t rotate the plane of the Slit Plate.)

23

24 CHAPTER 4. RAY OPTICS EXPERIMENTS

Record and explain your observations in terms of the straight-line propa-gation of light. Include a diagram showing how the width of the slit imagesdepends on the orientation of the Light Bulb filament with respect to the SlitPlate. Are the rays straight? How does the width and distinctness of each rayvary with the distance from the Slit Plate? How does the width and distinctnessof the slit images depend on the angle of the Slit Plate? For what angle of theSlit Plate are the images most distinct? For what angle are the images leastdistinct?

Figure 4.2: Ray tracing to locate the light bulb filament.

Use the fact that the light propagates in a straight line to measure thedistance between the Light Source filament and the center of the Ray Table, asin Fig. 4.2. The rays on the Ray Table all originate from the filament of theLight Source. Since light travels in a straight line, extend the rays backward tolocate the filament.

Tape a piece of blank white paper on top of the Ray Table and make areference mark on the paper at the position of the center of the Ray Table.Using a pencil and straight edge, trace the edges of several of the rays ontothe paper. Trace the rays back (using more paper if necessary). Measure thedistance between your reference mark and the point of intersection of the rays.Use the metric scale on the Optics Bench to measure the distance betweenthe filament and the center of the Ray Table directly. (The notch indicatesthe filament position.) How do these compare? Based on your observations,describe how light propagates through air.

4.2 Reflection

The shape and location of the image created by reflection from a mirror of anyshape is determined by just a few simple principles. One of these principles isthat light propagates in a straight line. In addition, observe the reflection of a

4.2. REFLECTION 25

single ray of light from a plane mirror and verify the Law of Reflection

θ1 = θ2, (4.1)

where the θi are the angles the ray makes with respect to the normal or per-pendicular to the surface before or after the reflection.

Figure 4.3: Optics bench configured for reflection tests.

Configure the equipment as shown in Fig. 4.3. Adjust the components soa single ray of light is aligned with the bold arrow labeled “Normal”; carefullyalign the reflecting surface of the mirror with the bold line labeled “Component.”With the mirror properly aligned, the bold arrow on the Ray Table is normal(at right angles) to the plane of the reflecting surface.

Rotate the Ray Table and observe the light ray. The angles of incidence andreflection are measured with respect to the normal to the reflecting surface, as inFig. 4.4. The plane that contains the incident ray and the normal to the mirroris called the plane of incidence. In this experiment, the plane of incidence is thetop surface of the Ray Table.

Figure 4.4: Measuring the angles of incidence and reflection.

By rotating the Ray Table, set the angle of incidence to 30 and measure


the angle of reflection. Comment on how well the angle of incidence and theangle of reflection agree with each other.

4.3 Refraction

What happens to the trajectory of a light ray that passes one medium to thenext? The direction of light propagation changes abruptly when light encountersa reflective surface. The direction also changes abruptly when light passes fromone medium to another. Observe the refraction or bending of a single ray atthe interface between two media and verify the Law of Refraction

n1 sin θ1 = n2 sin θ2, (4.2)

also known as Snell’s law, where the θi are the angles the ray makes with thenormal to the interface and the ni are the indices of refraction of the media.The numbers simply index the material. In this experiment, test the validity ofthis law, and also measure the index of refraction for acrylic.

Figure 4.5: Optics bench configured for refraction tests.

Configure the equipment as shown in Fig. 4.5. Adjust the components soa single ray of light passes directly through the center of the Ray Table De-gree Scale. Align the flat surface of the Cylindrical Lens with the line labeled“Component”. With the lens properly aligned, the radial lines extending fromthe center of the Degree Scale will all be perpendicular to the circular surfaceof the lens. (Check your alignment using what you already have learned aboutthe Law of Reflection.)

Without disturbing the alignment of the Lens, rotate the Ray Table andobserve the refracted ray for various angles of incidence. Is the ray bent whenit passes into the lens perpendicular to the flat surface of the lens? Is the raybent when it passes out of the lens perpendicular to the curved surface of thelens?

4.4. DISPERSION 27

By rotating the Ray Table, set the angle of incidence from 0 to 80 in10 increments. For each angle of incidence, measure the angle of refractionθA. Repeat the measurement with the incident ray on the opposite side of thenormal θB . Record your results neatly in a table in your lab notebook. Areyour results for the two sets of measurements the same? If not, to what do youattribute the differences?

In Igor Pro, combine both sets of data and plot the sine of the incidentangle versus the sine of the refracted angle. Find the slope and uncertainty of aproportional fit to the data. Compare with the accepted value for the refractiveindex of acrylic. Is your graph consistent with the Law of Refraction?

In performing the experiment, what difficulties did you encounter in mea-suring the angle of refraction for large angles of incidence? Was all the light ofthe ray refracted? Was some reflected? How did you use (or how might youhave used) the Law of Reflection to test the alignment of the Cylindrical Lens?How does combining the results of measurements taken with the incident raystriking from either side of the normal improve the accuracy of the results?

4.4 Dispersion

What if the effective speed of light in a material depends upon the color of thelight? In this experiment you will look at two phenomena related to refrac-tion. Dispersion complicates and enriches the Law of Refraction, because mostmaterials have different indexes of refraction for different colors of light.

Figure 4.6: Optics bench configured for dispersion tests.

Configure the equipment as shown in Fig. 4.5 so a single light ray is incidenton the curved surface of the Cylindrical Lens. Set the Ray Table so the flat sideof the lens is away from the light source and the angle of incidence of the raystriking the flat surface of the lens (from inside the lens) is zero degrees. Adjustthe Ray Table Component Holder so the refracted ray is visible on the ViewingScreen.

Slowly increase the angle of incidence. As you do, watch the refracted rayon the Viewing Screen. At what angle of refraction do you begin to notice


color separation in the refracted ray? At what angle of refraction is the colorseparation a maximum? What colors are present in the refracted ray? (Writethem in the order of minimum to maximum angle of refraction. Write only thecolors you actually see, not the ones you expect.)

Infer the index of refraction of acrylic for red and blue light using Eq. 4.2,remembering that here the ray passes from acrylic into air, not the other wayaround.

4.5 Total Internal Reflection

What happens to a light ray that cannot follow the Law of Refraction? Incertain circumstances light striking an interface between two transparent mediacannot pass through the interface. The result is total internal reflection.

Without moving the Ray Table or the Cylindrical Lens after completing theSection 4.4 dispersion observations, notice that not all of the light in the incidentray is refracted. Part of the light is also reflected. Record your observations,keeping the following questions in mind. From which surface of the lens doesreflection primarily occur? Is there a reflected ray for all angles of incidence?(Use the Viewing Screen to detect faint rays.) Are the angles for the reflectedray consistent with the Law of Reflection? Is there a refracted ray for all anglesof incidence? How do the intensity of the reflected and refracted rays vary withthe angle of incidence?

Very slowly rotate the Cylindrical Lens until all of the light is reflected (norefracted ray), and record this critical angle in your notebook. Compare yourobservation with the critical theoretical angle derived from Eq. 4.2.

Chapter 5

Wave Optics Experiments

Wave optics is the study of light in situations where its wavelength is not neg-ligible. In these experiments, investigate single slit diffraction, double slit in-terference, diffraction grating transmission, and exploit Babinet’s principle tomeasure the diameter of a strand of hair.

5.1 Single Slit Diffraction

Light spreads or diffracts around objects small compared to its wavelength likewater waves around boulders at a beach. Consider the Fig. 5.1 opaque barrierwith a slit of width w. Incoming electromagnetic radiation of wavelength λexcites electrons in the barrier inducing a secondary wave that interferes withthe incident wave to create a complicated diffraction pattern characterized bylight and dark fringes. Because plugging the slit would darken the far side, theexcited plug’s electromagnetic field must be the negative of the barrier’s field.Since intensity is proportional to the square of the field, the intensities due tothe barrier and the complementary plug must be the same, a result known asBabinet’s principle. Electromagnetic waves from different portions of the pluginterfere destructively at a distance D w to create intensity minima attramsverse positions

xj = D tan θj , (5.1)

where the angles θj satisfy

w sin θj = jλ, (5.2)

and the indices j ∈ ±1,±2,±3, . . . are non-zero integers.Configure the HeNe laser on the optics bench so that a light beam from

it passes through a single slit and projects the light intensity pattern for sin-gle slit diffraction onto a horizontal meter stick placed about one meter away.Illuminate single slits of width w = 0.02 mm, 0.04 mm, 0.08 mm, 0.16 mm.Qualitatively, how do the diffraction patterns vary with slit width w? Whathappens in the limit of large w λ and small w λ width?

29

30 CHAPTER 5. WAVE OPTICS EXPERIMENTS

I[x]

×10−4

Figure 5.1: The interference pattern of the slitted barrier excited by an incidentwave (left) is the same as that of the complementary excited plug (right). Slitand plug magnified 104 times.

Measure the distance D from one of the slits to the meter stick and thedistances x between the central maximum and several well-defined minima oneither side. In Igor Pro, plot jλ versus sin θj . assuming λ = 632.8 nm foryour HeNe. If the angles are small, the approximations sin θ ∼ tan θ ∼ θ 1simplify the work; if the angles are large, the data test the full nonlinear theory.Find the slope and uncertainty of a proportional fit to the data. Attach the plotto your lab notebook. Report the slit width w, its uncertainty, and its percentdifference from the labeled value.

5.2 Double Slit Interference

Consider the Fig. 5.2 opaque barrier with a pair of slits having width w andseparation d. Babinet’s principle implies that the interference pattern of thedoubly slitted barrier excited by an incident wave is the same as that of thecoherently excited plugs. Electromagnetic waves from the two plugs interferedestructively at a distance D w, d to create intensity minima at angles θisuch that

d sin θi =

(i+

1

2

)λ, (5.3)

5.3. DIFFRACTION GRATING 31

I[x]

D w ∼ d

×10−4

Figure 5.2: The interference pattern of the doubly slitted barrier excited by anincident wave (left) is the same as that of the coherently excited plugs (right).Slits and plugs magnified 104 times.

where the indices i ∈ 0,±1,±2, . . . are integers, including zero. For successiveminima near the central maximum, this implies

d∆x

D∼ d∆θ ∼ λ. (5.4)

The double-slit interference minima augment the single-slit diffraction minima.The total intensity is the product of the intensity of two coherent point sourcesand the diffraction pattern of an individual slit.

Replace the slide of single slits with the slide of double slits so that the lightbeam from the HeNe laser passes through the double slits and projects a patternonto the meter stick placed about two meters away. Inspect the light intensitypattern projected onto the meter stick. Qualitatively, how does the diffractionpattern vary with slit separation d? Use the double-slit minima to calculate theseparation of one pair of slits, and report the percent difference with the labeledvalue.

5.3 Diffraction Grating

A transmission diffraction grating consists of many closely spaced lines. Likeprisms, diffraction gratings can spread light into its component colors for anal-ysis. A single or double slit can be used to measure the wavelengths of light,but in practice a grating’s very sharp maxima provide superior resolving power.


D d w

I[x]

×10−4

Figure 5.3: The interference pattern of a grating excited by an incident wave(left) is the same as that of an array of coherently excited plugs (right). Gratingand plugs magnified 104 times.

Consider the Fig. 5.3 opaque barrier with an array of slits of width w andseparation d. Babinet’s principle implies that the interference pattern of thegrating excited by an incident electromagnetic wave is the same as that of anarray of coherently excited plugs. Electromagnetic waves from a coherent arrayof points interfere constructively at a distance D w d to create intensitymaxima at angles θi such that

d sin θi = iλ, (5.5)

where the indices i ∈ 0,±1,±2, . . . are integers, including zero. The diffractiongrating intensity maxima are at the same locations as the double slit maxima,but they are narrower and taller.

Place the diffraction grating in the holder so that the light beam from thelaser passes through the grating and projects the resulting intensity patternonto the meter stick. Be sure the meter stick is far from the grating. Observethe first order maximum from the grating using the laser, use it to calculate thegrating spacing, and report the percent difference with the labeled value.

5.4 Hair Strand

According to Babinet’s Principle, the diffraction pattern of a human hair isidentical to that of a slit in an opaque barrier (away from the light beam).

5.4. HAIR STRAND 33

Using Scotch tape, mount a strand of hair from yourself or your lab partner toan optics bench component holder. Place the hair 40 cm in front of the laser.Shine the laser on the hair and consider the diffraction pattern projected on themeter stick 1.0 m from the hair. Measure the distances x between the centralmaximum and several well-defined minima on either side. In Igor Pro, plot jλversus sin θj . Find the slope and uncertainty of a proportional fit to the data.Attach the plot to your lab notebook. What is your hair width?

If you have naturally curly hair, its cross section should be elliptical. Rotateyour hair in the laser beam. Does the diffraction pattern expand and contract?

Chapter 6

Simple Circuit Experiments

In these experiments, you will construct simple circuits involving light bulbsand a voltage source. Through these, you will develop an intuitive feel forthe behavior of light bulbs (and more generally resistors) arranged in differentconfigurations.

Throughout these experiments, you will be asked to make predictions. Youshould complete a full predicttestreflect cycle every time you are asked to make aprediction. This involves making a prediction in advance of making observations,briefly explaining your reasoning. Keep in mind that your prediction must beconcrete (stuff will change” is not a prediction) and testable. Then carefullytest your prediction. If your prediction is not correct, you should reflect and seewhere you might need to rethink a concept or incorporate some new concepts.Whether right or wrong, summarize any general principles youve learned fromthe test. You can learn a lot by making incorrect predictions so dont be afraidto be wrong!

6.1 Configuring the Voltage Source

Connect the red and black cables (one end with a banana plug and the other withan alligator clip) to the signal generator output on the Pasco interface. In DataStudio, click on the signal generator (right-most ports) and select “DC voltage”from the pull-down menu; this will apply a voltage that does not vary withtime. Turn off the “Auto” button and increase the voltage to 3V (equivalent totwo AA batteries). You can turn the voltage source on and off using the set-upinterface for the signal generator. To maximize the lifetime of the light bulb,you should only keep the voltage applied when you need to study your circuit.

You may find it useful to measure the current flowing through the signalgenerator. To do this, select “Measurements and Sample Rate”, un-select the“Measure Output Voltage” and select “Measure Output Current”. When youhit “play”, you will obtain a data set for current that you can plot or display in“digits”.

35

36 CHAPTER 6. SIMPLE CIRCUIT EXPERIMENTS

6.2 Using a Multimeter

You will want the flexibility to measure the current through or the voltage∆ϕ across any element in your circuit. To do this you will use a multi-meter,pictured below. To measure the voltage ∆ϕ across an element (for example,from one side of the light bulb to the other) you simply touch the probes to themetal connectors of the bulb holder as show in Fig. 6.1. To measure current, youneed to insert the multi-meter into the circuit, also shown in Fig. 6.1, so that thecurrent flowing through the multi-meter can be measured. In each quadrant,there are multiple settings, which indicate the maximum voltage/current thatcan be measured. If the value exceeds that limit you will see a “.OL” messageon the screen.

Figure 6.1: Measuring voltage across a light bulb (left) and current through alight bulb (right).

6.3 Current Flow in a Circuit

Construct the circuit in Fig. 6.2, which includes just one light bulb. The bulbacts, to some degree, as a “visible” resistor. As current flows through thebattery, the light bulb filament heats up; the higher the current through thebulb, the brighter it will be. Thus the brightness of the light bulb will provide anice visual indicator of the current in our more complicated circuits. Note: The

6.4. SERIES AND PARALLEL RESISTORS 37

brightness is not proportional to the voltage, so you can only gauge whether thecurrent has increased or decreased, but is it difficult to infer how much it haschanged.

Figure 6.2: Simple circuit configuration A.

Use the multi-meter to measure the voltage ∆ϕ across the light bulb. Howdoes this compare to the voltage setting in Data Studio?

Measure the current as it leaves the signal generator and flows into the bulb,and as it leaves the bulb and flows to the signal generator. What happens tothe current as it flows through the bulb? Does the current get “used-up” by thebulb?

The current flowing through the signal generator is fundamentally relatedto what is called “effective” resistance Re of a circuit defined by

∆ϕ = IRe. (6.1)

In this experiment, the voltage∆ϕ = 3.0V at all times. As you will learn in class,there are mathematical ways to calculate Re; the purpose of this experimentis to develop an intuition for what Re means and how it is affected by theconfiguration of a circuit.

What is the effective resistance of this single light bulb? Note: Light Bulbsdo not behave in the same way as true resistors. Next week we will explore therelationship between voltage, current, and resistance more rigorously. All theresults you obtain today are useful, but only qualitative.

6.4 Series and Parallel Resistors

If you have two more elements in your circuit, there are two general configura-tions: series and parallel, shown on the left and right of Fig. 6.3. When thelight bulbs are in series, the current passes through one bulb and then the other,before flowing back to the negative terminal of the voltage source. When thelight bulbs are in parallel, each light bulb is connected to both the positive andnegative ends of the voltage source. Construct each of these circuits (B and C),so that you can easily hook each up to the voltage source for easy (and quick)comparison.


Figure 6.3: Series and parallel circuit configurations B (left) and C (right).

Connect the “Series” configuration to your voltage supply. How do theintensities of bulbs #2 and #3 compare to each other? How do they compareto bulb #1 (in previous circuit)?

Measure the current through each bulb using the multi-meter; how do theycompare to each other and to the current flowing through the signal generator?

Measure the voltage ∆ϕ across each bulb. How do they compare to eachother and to the voltage supplied by the signal generator?

Predict what will happen to the current flowing through both bulbs and thesignal generator, if you unscrew bulb #2. Remember to Predict Test Reflectwhen asked to make a prediction.

Now connect the “Parallel” configuration to the voltage supply. How do theintensities of bulbs #4 and #5 compare to each other? How do the intensitiesof this bulb compare to bulb #1? What does this suggest about the currentflowing through bulbs #4 and #5?

Based on previous results, predict the current flowing through bulbs #4 and#5 and also the current through the signal generator (no peaking!) as well asthe voltage ∆ϕ across bulbs #4 and #5. (Note: These bulbs are not identical,so you should expect some differences.)

If you unscrew Bulb #5, predict what will happen to the current throughBulb #4 and the current flowing through the signal generator.

For each circuit, use the current readings from the signal generator to findthe effective resistance of the circuit. How do these effective resistances compareto the effective resistance of a single bulb?

6.5 More Complex Resistors

Now consider the more complex circuitsof Fig. 6.4. Before you even constructthe circuit, make a prediction about how the brightness of bulbs #6-8 willcompare to each other, and how they will compare to bulb #1. Explain yourreasoning thoroughly!

Measure the voltage ∆ϕ across each of the bulbs and the current througheach bulb. Is the voltage ∆ϕ across each parallel branch of the circuit roughly

6.5. MORE COMPLEX RESISTORS 39

Figure 6.4: Complex circuit configurations D.

the same? (Measure the voltage ∆ϕ from a point just before bulb #6 to a pointjust after bulb #7.)

Is the current flow through each branch the same? If not, which is higher?(How could we tell this without even measuring the current?) Why does thecurrent behave in this way?

Predict what will happen to the current through bulbs #6 and #8 if bulb#7 is unscrewed. Also predict what will happen to the current through bulbs#6 and #7 if you unscrew #8. You may be surprised by the result, so thinkvery carefully about what you have observed.

Finally, consider the circuit pictured below. In this case, bulbs #10 and 11are in parallel with each other and the combination of #10 and 11 is in serieswith #10. The combination of #9-11 is in parallel with #12, but none of thesebulbs are individually in parallel with #12. We would say that #9-11 are ina branch that is parallel to #12. As before, predict the relative brightness ofthese four bulbs (#9-12) before you even construct the circuit.

Figure 6.5: Complex circuit configurations E.

Now supply current to your circuit. If some of your bulbs are not receivingenough current to be visible, try momentarily increasing the voltage to 5V.However, dont leave it at this setting for long or you may blow out Bulb #12.Were your predictions about the brightness correct?

Measure the voltage ∆ϕ across each bulb and compare them to each other


and to the voltage supplied by the signal generator. Consider all the differentpaths that the current can possibly take. If you add up all the voltage ∆ϕ sacross all the elements on each pathway, how does this compare to the voltagesupplied by the signal generator?

Predict what will happen to the brightness of the remaining bulbs when bulb#11 is unscrewed. Be very specific, including predictions of which bulbs willget brighter/dimmer or remain the same.

Measure the current supplied by the generator and the current through bulbs#9, 10 and 12 when bulb #11 is in place and when it is removed from thecircuit. How can you use what you have learned in this experiment to explainthese changes in current as bulb #11 is added and removed from the circuit?

Measure the Voltage ∆ϕ across bulbs #9, 10, and 12 when bulb #11 is inplace and when it is removed. Which of the voltage ∆ϕ s change and how?Which remain the same? Why does this make sense?

Summarize your observations by briefly addressing the following questions:When two elements in a circuit are connect in series, which property (voltage

or current) is the same for the two elements? What is the same for elementsthat are in parallel?

How doe the effective resistance depend on the configuration (series or par-allel)? Why should it matter (physically) how the resistors are added into thecircuit?

Is the amount of current flowing through the generator fixed (like the voltage∆ϕ )? What ultimately determines how much current flows through the circuitand how it is divided up among the different paths?

Chapter 7

Ohm Experiment

By 1827, Georg Ohm had discovered [4] that in many cases voltage across anobject is proportional to the current through the object. As a consequence, theSI unit of resistance is named for him.

Mathematically, the current I through a material is proportional to theelectric potential difference or voltage ∆ϕ across it, so that

I =1

R∆ϕ (7.1)

or∆ϕ = IR, (7.2)

where the resistance R depends on the material. If R is constant, the materialis ohmic. If R is not constant, the material is non-ohmic. A plot of voltage∆ϕ versus current I is a straight line through the origin for ohmic materials butis nonlinear for non-ohmic materials.

7.1 Ohmic Resistor

Use Data Studio to plot voltage versus current for two resistors on the PASCORLC board. Use the Data Studio signal generator window to apply an increasingramp voltage from +5V to −5V at 2Hz. Acquire data for a couple of seconds,and then stop recording and turn off the signal generator so it doesn’t overheat(and to avoid excess data). Compare the slopes of your plots with the resistancesread from resistor codes in Appendix C. What are the relative differences?

7.2 Light Bulb

Repeat the previous analysis for a light bulb on the RLC board, but this timesystematically vary the frequency of the increasing ramp voltage from about0.5Hz to about 20Hz. Can you explain the changes? Is the light bulb an ohmicor non-ohmic device – or is it not that simple?

41

42 CHAPTER 7. OHM EXPERIMENT

7.3 Diode

Repeat the previous analysis for the “diode” on the RLC board. What is goingon? It should be spectacular.

Figure 7.1: An ideal diode allows current to flow in only one direction.

A simple diode consists of two semiconductors contaminated or dopedwith other atoms so that the N-type semiconductor has excess negative chargesor electrons and the P-type semiconductor has a deficit of negative chargesor an excess of positive holes. A battery or other voltage source connected oneway attracts the positive holes to its negative terminal and attracts the negativeelectrons to its positive terminal, and no current flows across the junctionbetween the semiconductors, as on the left of Fig. 7.1. However, a batteryconnected the other way repels positive holes from its positive terminal andrepels negative electrons from its negative terminal, and the electrons fill theholes at the junction allowing current to flow, as on the right of Fig. 7.1, withnew electrons and holes appearing to replace the annihilated ones. For lightemitting diodes or LEDs the annihilation of the electrons and holes producesvisible light.

Bi-colored bi-directional LEDs are actually two opposing diodes in par-allel. They are convenient indicators of current flow in circuits.

Appendix A

Formal Report Guide

Form and contact converge in the next four pages, which contain instructionsand tips for creating a professional-looking physics report in the form of a sci-entific paper.

43

44 APPENDIX A. FORMAL REPORT GUIDE

This is a descriptive title

Your Name, Partner Name

Physics Department, The College of Wooster, Wooster, Ohio 44691, USA

Day Month Year

Abstract

The abstract should state very concisely (usually in one paragraph) the scope and nature of the

subject discussed, the basic method or approach, and a summary of the major results. It is more

valuable for the reader to learn, for example, that “we calculated the speed of light to be

2.97 ± 0.03( ) !108m/s, which is within 0.67% of the accepted value” than to read that “the speed

of light was measured”. The abstract should stand alone without reference to the rest of the

paper, since many people will read only your abstract and not the full paper.!

1

45

I. INTRODUCTION

The introduction should outline for the reader exactly what is to be discussed in the paper, the

purpose of the work, and a brief history [1-2] of previous work relevant to the investigation [3].

Here the authors of an original research paper can describe what is new in their work and how it

contributes to the field.

II. THEORY

Experiments are designed and performed within a theoretical context. Describe this context

here and summarize, motivate, or derive the relevant equations.

Equations should be treated like words in sentences. They should not stand outside sentences,

but should be punctuated as words inside the sentences, even when they are indented and

numbered. For example, if

!

ax 2 + bx + c = 0,! (1)

then

!

x = !b ± b2 ! 4ac2a

.! (2)

To preserve the tabs in these equation lines, copy, paste, and edit them to create other equations.

Use superscripts for exponents in scientific notation. Be sure to explain what each symbol

means. Do not assume the reader knows what F or i means. When referring to variables in a

sentence, they are traditionally italicized (as in the previous sentence).

III. PROCEDURE

Briefly describe what you did in full sentences and complete paragraphs. Do not write this

2


section as a numbered list of steps, and do not imitate a lab manual! Typically use the past tense.

Figures of the apparatus, including either schematics or digital photographs, are often valuable

here, but all figures should be numbered, captioned, and references in the text. Serial numbers of

each piece of equipment are not necessary, but you should identify the major equipment used.

This is also the place to describe experimental difficulties and how (or whether!) they were

overcome and any corrections or calibrations which were used.

IV. RESULTS

Concisely summarize your results and discuss them. This section will probably include plots

and tables to display your results. Plots and tables do not stand alone; each one must be discussed

in the text. For example, soliton speeds decrease monotonically with angle, as in Fig. 1. Guide

the reader through the important things to notice when looking at the figure.

FIG. 1: Simulated soliton speeds as a function of angle. The dotted curve is a phenomenological fit. Inset depicts velocity vectors. Blue and red colors indicate positive and negative modes.

All graphs, figures and tables must be labeled and captioned. Graphs must be titled, tables

should have headings, and both should be labeled with units. Graphs and figures should be large

enough to be clear; include error bars in your graphs. Graphs and tables should be on the page

they are first mentioned or on the next page, not appended to the end of the report. Verify that

3

47

your results (including slopes of graphs) have proper units, the appropriate number of significant

figures, and uncertainty estimates. For example, “We estimate Planck’s constant h to be

7.0 ±1.9( ) !10"34 J # s, which is within one standard deviation of the accepted value”. Typically,

you will not include in your report all the raw data in your lab notebook.

V. CONCLUSIONS

In some cases the purpose of the experiment is the measurement of specific quantities (for

example, Millikan Electron Charge or The Speed of Light). Your result should be compared,

whenever possible, with previously measured values, handbook or textbook values, or a

theoretically calculated result. You should indicate the extent of agreement or disagreement and

discuss any discrepancies.

In other experiments (for example, Franck-Hertz Energy Quantization) an important aspect

of the investigation is to illustrate an effect or to distinguish between rival models or theories.

Here is where you should draw conclusions based on your data. This may also involve a

discussion of uncertainties. In some cases you may have to say that no conclusions can be drawn

from your data. You might also suggest possible improvements in the experiment.

Acknowledgments

If you borrowed apparatus from another laboratory, obtained ideas in discussions with others, or

had financial support for your experiment, you should acknowledge such assistance here.

!

[1] J. F. Lindner, A. R. Bulsara, Phys. Rev. E 74, 020105 (2006).

[2] J. F. Lindner, K. M. Patton, P. M. Odenthal, J. C. Gallagher, B. J. Breen, Phys. Rev. E 78,

066604 (2008).

[3] A. A. Fuki, Y. A. Kravtsov, O. N. Naida, Geometrical Optics of Weakly Anisotropic Media

(CRC Press, 1998)

4

Appendix B

Electromagnetic Units

Although best for practical applications, SI units obscure the symmetry andelegance of electromagnetism and are not used in advanced texts. Table A-1summarizes familiar electromagnetic equations in three commonly used systemsof units.

Table A-1: Key electromagnetic equations in three common systems of units.Natural Gaussian SI

E =Q

4πr2E =

Q

r2ε0E =

Q

4πr2

B =I

2πsB =

2

c

I

sµ−10 B =

I

2πs

~F = q(~E + ~v × ~B

)~F = q

(~E +

~v

c× ~B

)~F = q

(~E + ~v × ~B

)

ΦE = Q ΦE = 4πQ ε0ΦE = Q

ΦB = 0 ΦB = 0 ΦB = 0

ΓE = −ΦB ΓE = −1

cΦB ΓE = −ΦB

ΓB = +ΦE + I ΓB = +1

cΦE +

1

cI µ−10 ΓB = ε0ΦE + I

49

50 APPENDIX B. ELECTROMAGNETIC UNITS

Appendix C

Resistor Units

The most common resistors are little cylinders of carbon with a wire attachedto each end (the leads). Although the leads have some resistance, it is negli-gible compared with the resistance of the carbon cylinder (remember, a smallresistance in series with a large resistance can be ignored). Ordinary carbon re-sistors have colored bands on them that indicate the resistance in ohms. Thereare usually four bands-three colored bands, followed by a silver or gold band.Reading toward the gold or silver band, the color codes are listed in Table A-1.

Table A-1: Resistor codes.

Band 1 2 3 4Color Digit Digit Multiplier Tolerance

Silver - - 10−2 10%Gold - - 10−1 5%Black 0 0 100 -Brown 1 1 101 -

Red 2 2 102 -Orange 3 3 103 -Yellow 4 4 104 -Green 5 5 105 -Blue 6 6 106 -

Violet 7 7 107 -Grey 8 8 108 -White 9 9 109 -

The tolerance (or precision) is indicated by the fourth band. Silver indicatesa 10% tolerance, while gold indicates a 5% tolerance. Hence a 27kΩ resistor(27,000 ohms) has a red band nearest the end of the resistor, then a violetband, then an orange band, and finally, if it has a 10% tolerance, a silver band.

51

52 APPENDIX C. RESISTOR UNITS

Bibliography

[1] Augustin de Coulomb, “Premier Memoire sur l’Electricite et le Magnetisme(First Memorandum on electricity and magnetism)”, Histoire de l’AcademieRoyale des Sciences (History of the Royal Academy of Sciences), 569-577,1785.

[2] Andre-Marie Ampere, “Memoire de l’action mutuelle de deux couranselectriques” (Memorandum of the mutual action of two currents)”, Annalesde Chimie et de Physique (Annals of Chemistry and Physics), 15, 59-76,1820.

[3] Michael Faraday, Experimental Researches in Electricity, Vol. II, page 164,Richard and John Edward Taylor, London, 1844.

[4] Georg Simon Ohm, Die galvanische Kette: mathematisch bearbeitet (TheGalvanic Circuit Investigated Mathematically), Riemann, Berlin, 1827.

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