Nikola Tesla taking notes in his ColoradoSprings lab in December 1899. Photo by Dick-enson V. Alley (copyright expired).

ELECTROSTATICSPhysics 241/261

Winter 2012

1 IntroductionMany of the objects we rely on daily—such as cars, TVs, and computers—rely on the behavior of theelectromagnetic force to function. Here, we will begin to study this force by examining the behavior ofnon-moving charges and charges in equilibrium, a field of physics called electrostatics.

We will explore three different electrostatic effects (see Figure 1):

1. Charging by conduction (or direct contact): A charged object is brought into contact with an un-charged one. Charge spreads across both objects, which are then separated. See Figure 1(a).

2. Polarization: A charged object near a neutral object separates positive and negative charges slightlyin the neutral object, as seen in Figure 1(b). As a result, the charged object and the oppositelycharged near side of the neutral object will be attracted to each other. Note that the neutral objectremains neutral overall.

3. Charging by induction: A wire connected to the ground can be used to drain off extra charge fromone side of a polarized object, leaving it with a net charge, as seen in Figure 1(c).

As you work through the lab, think about where the charge is going and which of these effects areimportant.

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−−−

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F F

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Figure 1: (a) Charging by conduction, or direct contact. (b) Polarization. (c) Charging by induction.

To perform our studies of electrostatics, we first will learn how to use an electroscope (Section 4) andhow to determine charge polarity (Section 5). We will then examine how charges distribute themselves ona conductor, in this case a metal can (Section 6). By observing the discharge of a charged electroscope,we will be able to determine the sign of the charge carrier and whether electrons or protons move moreeasily (Section 7). We will see how to charge an object both directly (Section 8) and through induction(Section 9). We will also investigate how a flame can discharge a charged object (Section 10). Finally, wewill experiment with a water dripper apparatus and determine how it is capable of building up a charge(Section 11).

By the end of this lab, you should be familiar with these three effects. In particular, you shouldunderstand the difference between polarization and induction. You should have an understanding of howthe water-dripper experiment works (Section 11) and how Section 7 demonstrates that electrons do themoving when charge is transferred.

2 TheoryBefore starting this lab, you should be familiar with the following physical concepts. If you need to reviewthem, or if you haven’t yet discussed them in your lecture course, consult the indicated sections in Young& Freedman, University Physics.

• Electric charge, §21.1

• Inductors, conductors, charging by induction, polarization §21.2

You may also find it useful to review §21.3.

3 Equipment• electroscope with built-in or external deflection scale

• UMHVPS low-current, high-voltage power supply (To avoid risk of shock, do not substitute withany other power supply!)

• insulated disk; insulated platform; round can

• water dripping apparatus: ring stand, insulated loop, water can with valve

• matches; screen; aluminum foil; mylar; glass plate

• banana cables and alligator clips

3.1 ElectroscopeThe electroscope, used to hold and measure charge, is shown in Figure 3. The round plate on top of theelectroscope is attached to the movable vane inside the electroscope. These are insulated from the outercase. When there is charge on the top plate and movable vane, the vane will turn on its hinge as the chargesrepel each other and attempt to spread out. A greater amount of charge will cause the vane to deflect to agreater degree.

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Figure 2: Power supply.

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Figure 3: Electroscope.

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Figure 4: Charging the electroscopes by direct contact. Note: When appropriate, sight down along thevane to read the angle scale.

3.2 Power SupplyIn the lab, charge will be created using a power supply like that shown in Figure 2. The high voltagepower supply device has three terminals: the negative; the mid-point (common or ground); and the positivevoltage terminals. There exist relative voltages between these three terminals that depend on the settingof the voltage dial. However, no particular relationship exists between these three terminal voltages andany other objects in the laboratory including the case of the power supply. Therefore, any of the threeterminals can be connected to the external point that you choose as your reference for zero potential.In this experiment, the case of the electroscope will be the reference for zero potential. With any leadconnected to this reference, the other two leads provide a potential difference relative to the zero potentialpoint. Remember, you are connected to the zero reference point while standing on the lab floor or touchingobjects in the lab, so treat the two leads not connected to the reference with respect. Each of the terminalscan be considered as an infinite reservoir of charge relative to the other two. With respect to the mid-pointor positive terminal, the negative terminal supplies negative charge. The positive terminal supplies positivecharge relative to the negative or mid-point terminals. The voltage between the three terminals and hencethe charge provided depends on the setting of the silver voltage dial. The voltage reading indicates thedifference between the positive and negative terminals. The common or ground is midway between thenegative and positive and has one half the readout voltage value relative to either of the two extremes.

In ALL the following experiments, you must be SURE that one (and only one) terminal of your powersupply is connected to ground (the case of the electroscope). Which particular terminal is grounded willvary from experiment to experiment. We will call the non-grounded lead the HV lead.

4 Experiment: Calibrating the Electroscope

4.1 ProcedureFigure 4 shows the way to connect the electroscope to charge it with the power supply. Tap lightly onthe electroscope case to make sure the movable vane can turn freely on its hinge. Connect the negativeterminal (blue) of the power supply to the electroscope case with a wire and clip. Recall from our dis-cussion in Section 3 that whichever lead from the power supply is connected to the electroscope case isdefined as ground, or the zero potential point. Therefore, a wire coming out of the positive lead is positiverelative to the electroscope case. Turn the voltage on the power supply all the way down; if you haven’talready, connect another lead from the + terminal of the power supply to the top plate of the electroscope.Hereafter, we will refer to the wire not connected to the electroscope case as the HV lead. Note: avoidtouching the insulator between the top plate and case of the electroscope; sweat and grease may allowcharges to leak across.

Turn on the power supply and turn up the voltage with the silver control knob (voltage will be indicatedin kilovolts on the power supply meter). You should observe deflection of the vane. Remove the HV wirelead from the electroscope and watch the vane for a minute or so. If the deflection decreases visibly duringthat time (by 10◦ or so), charge is leaking from the electroscope. This is only likely to be a problemduring humid weather, and can be cured by gently warming the electroscope with a hair dryer (consultyour instructor or ask at the supply window). You may also wish to wipe off the insulator between the topplate and electroscope case.

Make measurements of the electroscope deflection for several positive high voltage values. Comparewith deflections for a few negative supply voltages on the top plate of the electroscope. In this second casethe ground reference must be connected to the positive lead of the power supply. Make sure to turn thevoltage all the way down before exchanging leads at the power supply.

4.2 AnalysisMake a graph of deflection vs. voltage. Was the deflection linearly related to the voltage? What does itmean if your deflection at zero volts isn’t zero? An ideal measuring device has a linear response. Estimatethe deflection necessary before the electroscope has a reliable reading.

5 Experiment: Determining the charge polarity

5.1 ProcedureIn the above experiment, you know the polarity (sign) of the charge on the electroscope; that is, you assumeit matches the polarity of the charge you supplied. For some of the following experiments, however, youwill need to determine the polarity. To determine how we should do this, test three cases:

1. Set the power supply to 4.0 kV and charge the electroscope using the + terminal as the HV lead.Carefully remove the HV lead from the electroscope. To test the polarity, bring the HV lead nearthe end of the movable vane without touching it. Remember to hold the lead by the insulated part,and don’t touch any other metal objects. Record what happens.

2. Re-charge the electroscope, then remove both the positive and grounded leads (remember that thecase of the electroscope is our ground). At this point, the electroscope should be charged (is it?).Turn off the power supply and connect the positive lead to the electroscope case; this basicallyswitches the HV and ground leads. Turn the power supply back on, and hold the HV lead near thevane – do you see what you expect?

3. Next, discharge the electroscope by touching your hand to the top disk and the case (which is ourzero potential reference) simultaneously. Do not do this with the power supply connected! Nowbring the HV lead (charged either to + or −) near the vane. Record what happens.

4. Finally, charge the electroscope again with the positive lead as the HV lead. After charging, removethe ground lead and bring the HV lead near the vane to test polarity. Repeat this process a few timeswith each lead and record what happens.

5.2 AnalysisIn case 3 you should have seen an attraction. What causes the neutral vane to be attracted to the HV lead?Hint: see Figure 1(b).

In case 4 you may not find that you get the same results each time you test for polarity. You will likelynot see the result that you expect. If you find that you get a result you did not expect, can you explainwhy?

We looked at four different cases that resulted in attraction or repulsion of the vane by the HV lead.Given your results, what is the only way to be sure the vane is charged and that you know what sign thecharge has?

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Empty can

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Figure 5: Charging the can by contact.

6 Experiment: Distribution of Charges on a Conductor

6.1 ProcedureSet up as shown in Figure 5. Discharge the electroscope and then connect the negative terminal, blue, tothe electroscope case as your zero potential reference. The positive terminal, red, will be your high voltagelead. Connect this high voltage lead to the insulated three-legged platform and set a round empty can onthe platform. Turn the voltage to its maximum: there will now be a distribution of charge on the can.

We will find the distribution of charge by the following method: holding the small insulated disk byits handle, touch the disk to the top rim of the can and then to the top disk of the electroscope. Charge willbe transferred from the can to the disk, and then from the disk to the electroscope. Repeat until you cansee a sizable deflection—record the deflection and how many trips the disk made. Determine the polarityof the charge on the electroscope.

Discharge the electroscope and repeat the experiment, this time touching the disk to the inside of thecan.

Discharge the electroscope once more, and then transfer charge from the outer side of the can.

6.2 AnalysisHow much charge was transferred per trip of the disk for each location (rim, outside, inside)? From thisinformation, where is the most charge concentrated on the can? Where is the charge the smallest? Wasthe charge always the same polarity (positive/negative)? Use physics to explain why you saw the chargedistribution you did.

7 Experiment: Discharging Through the Air

7.1 ProcedureFirst, charge the electroscope with a negative voltage. To do this:

1. Remove both leads from the electroscope.

2. Connect the positive lead to the electroscope case, establishing a new zero potential (i.e., ground)reference.

3. Clip the negative lead onto the electroscope disk, and give the electroscope a negative charge.

4. After charging the electroscope, remove both leads (make sure the electroscope remains charged)and clip the negative lead to the case of the electroscope.

The positive terminal is now a source of positive charges. Cut a narrow wedge of aluminum foil, andturn off the power supply. Grab the foil wedge with the positive HV clip (Figure 6) and turn on the powersupply, so that there is positive charge on the point.

Position the foil wedge about 10 cm above the top plate, and bring it slowly closer. Observe the distanced at which the electroscope discharges. Note that we want a complete discharge of the electroscope – whenyou move the foil wedge away, the vane should stay at the zero position!

Repeat the experiment with the positive and negative terminals interchanged so that the charge on theelectroscope is positive and the charge on the point is negative as it is brought near the electroscope disk.(Try to use the same voltage settings. If the scope is too sensitive, you may need to turn down the voltage,but consider this when discussing your results!) Again record the distance needed for discharge.

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Aluminum foil-sharp pointElectroscope

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Figure 6: Discharging with an aluminum foil point.

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Figure 7: Charging by induction.

7.2 AnalysisIn order for the electroscope to discharge, charge had to move through the air from the foil wedge to thescope, or vice versa. Our data, together with these two pieces of information:

1. A large electric force is necessary to pull charges out of a metal (such as the aluminum wedge or thetop plate of the electroscope).

2. Electric forces are higher near sharp points than near flat surfaces.

are enough to tell us whether electrons (negative charges) or nuclei (positive charges) are actually doingthe moving. (If you have already done the Electric Fields lab, you can help yourself understand thesefacts by drawing the field lines between the sharp point and the top plate of the electroscope.)

Using the above facts, construct an argument to support this statement: “If electrons move more easilythan nuclei, the negatively charged foil wedge will discharge the electroscope at a larger separation thanthe positively charged wedge will.”

Do your data support the conclusion that electrons move more easily than nuclei?

8 Experiment: Charging by Direct Contact

8.1 ProcedureTurn the power supply down from its maximum setting to a more reasonable level before proceeding withthe remainder of the lab. Discharge the electroscope. Attach the negative lead to the electroscope case,and attach the HV lead to the insulated platform. As you did for the empty can, use the insulated disk totransfer charge from the platform to the electroscope.

8.2 AnalysisNote how much charge is transferred by conduction. (This will be compared to observations in the nextsection, which explores charging by induction.) Also, note the polarity of the transferred charge.

9 Experiment: Charging by Induction

9.1 ProcedureDischarge the electroscope. Again, put the negative lead on the electroscope case and the positive on theinsulated platform (not the electroscope top plate!). Hold the insulated disk a small distance above theplatform. The disk will be polarized—draw a quick sketch that illustrates the distribution of the charges.Next, connect another wire to the power supply negative terminal. This wire is now also a zero potentialreference. Touch it briefly to the top surface of the insulated disk, while the disk is polarized (see Figure 7).Remember that any of the three terminals of the power supply should be thought of as a large reservoir ofcharge. Where would charge move while the back of the disk is grounded? Draw another quick sketch.Touch the disk to the electroscope to measure its charge. Test for polarity.

9.2 AnalysisUsing the sketches requested above, explain how the disk becomes charged without touching the platform.What sign do you expect for the charge on the disk? Is that the sign you measured?

How does charging by induction compare to charging by conduction (the previous experiment)? Whichtransfers more charge?

10 Experiment: Discharging Effect of a Flame

10.1 Procedure and AnalysisWith the negative terminal, blue, connected to the electroscope case, charge the electroscope to +3000 Vor more and remove the positive HV clip. Light a match and position the flame near the disk of theelectroscope. The scope discharges! Try to determine experimentally what causes this effect. Here aresome things that might be the cause:

1. Light from the flame.

2. Ions (charged atoms) produced in the flame, then drawn to the electroscope.

3. Heat from the flame.

4. Air currents from the flame.

Come up with tests to eliminate all but one possible cause. Describe what you tried, and why. Whenyou have decided on the most likely cause, come up with a test that proves you are right.

Some tests you might make are: changing the charge on the electroscope to the opposite sign, holdinga glass plate between flame and electroscope, holding the high voltage clip with a wire mesh attached overthe flame (to compete with the electroscope by drawing charges from the air).

11 Experiment: Charge Transport by Water Droplets

11.1 Procedure and AnalysisAssemble the apparatus shown in Figures 8 and 9. An insulated metal ring is held so that the water dropsfall through it. The top of the ring should be level with the tip of the dripper nozzle. The droplets fall into

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Figure 8: Water-dripper setup.

the can which sits on the insulating platform and is connected to the disk of the electroscope. Note: Thenozzle tip should not be inside the ring. Any, even slight, electrical leakage will prevent this from workingwell. Do not let water splash around and get insulators wet; especially keep the feet of the round platformdry. Arrange the lead from the can to the electroscope so that it does not touch anything else, includingthe table or other wires.

Turn up the voltage to the ring to 4500 V; start the water dripping fast (but by drops, not in a steadystream) and watch the electroscope. Does it become charged? If so, is the sign of the charge the same asthat delivered to the metal ring? Test it.

Investigate how the operating conditions affect the dripping and charging rates. First, move the ringto positions above and below the nozzle. What are the charging rates at these positions? Return thenozzle to the original position. Second, vary the drip rate from very slow to a constant stream by openingand closing the nozzle. What are the charging rates? Third, vary the voltage on the ring. How does thecharging rate vary with ring voltage?

How large can you build the electric charge on the electroscope using this apparatus? Can you make itlarger than you could with the power supply alone? Why? Where does the charge come from?

Figure 9: Charge transport setup. Note that the negative terminal of the power supply is grounded to boththe electroscope case and the dripper stand, and that the can and platform are connected to the top plate ofthe electroscope.