Washington University in St. Louis Electrostatics Lab Introductory Physics Lab Summer 2018

Electrostatics: The Shocking Truth

STOP Important health warning for students with pacemakers or other electronic medical devices:

This lab involves the use of a Van de Graaff generator, which produces small amounts of electrical charge. They are regularly used in elementary schools, high schools, colleges, and science centers. They pose no risk to health or safety, except to students with pacemakers or other electronic medical devices. If you use a pacemaker or other electronic medical device, please contact the Lab Manager, Merita Haxhia at [email protected], IMMEDIATELY to make other arrangements for lab. It is very unlikely that you will be affected, but safety is our top priority. As long as you do not have this type of medical device, you have absolutely nothing to worry about. However, it is not recommended that you bring sensitive electronic equipment to this experiment.

Pre-Lab: The Van de Graaff Generator

A Bit of History

The Van de Graaff generator is an electrostatic generator, capable of producing constant electric potential differences reaching about 10 million volts. The model that you will use (thankfully) only achieves about 1% of that. The term Van de Graaff electrostatic generator may sound a little foreign, but there is one electrostatic generator that you are no doubt familiar with: earth’s atmosphere. In fact, some of the most famous experiments in the history of electrostatics were done using the atmosphere. In May of 1752, Benjamin Franklin performed his well-known kite experiment, an experiment which strongly suggested that lightning might not be so different from the sparks he produced using silk and glass. Interestingly, not long after Franklin completed his experiment, he learned that he had been scooped by a group of Frenchmen who had read one of his recently published books. It turns out that both groups were lucky to survive the experiments, as a Swedish scientist died the next year while attempting to replicate them.1

The Van de Graaff generator itself has achieved great fame as a tool for demonstrating the principles of electrostatics to physics students in spectacular fashion. (The world’s largest Van de Graaff generator, found at the Boston Museum of Science, exists solely for this purpose.) However, the Van de Graaff generator has also been used as a tool for doing real science ever since its invention by the American physicist Robert Van de Graaff around 1930. The high potential differences produced by large Van de Graaff generators are still used as particle accelerators around the world. While they can’t accelerate particles to energies of a TeV (1 trillion electron volts) like the Large Hadron Collider at CERN, sometimes a few MeV’s (millions of electron volts) is all a researcher needs. Among the many modern uses for the Van de Graaff generator are radiocarbon dating, x-ray imaging, and the production of particles for medical purposes.2 Current

Research 1 Washington University in St. Louis Electrostatics Lab Introductory Physics Lab Summer 2018

The Van de Graaff generator even played a role in a recent research project in which the Wash U physics department played a major part.3 The Stardust mission sent a spacecraft through a comet tail, collected particles that had blown off the comet, and safely landed back on earth. In order to calibrate their collectors, scientists bombarded them with small grains accelerated to speeds up to 30 km/s. Such incredible speeds could most efficiently be produced using large Van de Graaff generators. See the lab website for a link to more details.

University of Virginia Van de Graaff Resource

The big piece of equipment in this week’s experiment is a Van de Graaff generator powered by a hand crank. A Van de Graaff generator uses some clever tricks in order to charge a metal dome to a very high potential.

The University of Virginia has an excellent virtual demonstration of the inner workings of the Van de Graaff generator. You can find a link to this demonstration on the Pre-Lab Links page on the lab website. Walk through the presentation (that is, watch the videos and read the slides) and answer the following questions. (Remember, you must complete the Pre-Lab quiz on Blackboard. You will not turn in a physical copy of your responses to these questions.)

PL1. What is the only quick way to discharge a fully charged Van de Graaff generator?

PL2. What is the function of the motor of the Van de Graaff generator?

PL3. Why won't a Van de Graaff generator work if the pulley and the belt are made of the same material?

PL4. The outside of the belt carries electrons upward toward the dome. Where do these electrons come from?

PL5. How can electrons jump from the outside of the belt onto the upper comb that is attached to the dome? Why aren’t they repelled by the excess electrons that are already on the dome?

PL6. How could you make a Van de Graaff generator with a positively charged dome?

Completing This Lab Without a Computer

The Electrostatics Lab will be completed without a computer. Here are some requests. STOP • It would be very helpful for you to bring your own printout of the manual to the lab. It’s only four pages if you print pages 3 through 9 using a double-sided printer. • Please bring a notebook in which you can write your lab report. • It is possible for the Van de Graaff generators used in this experiment to damage electronic devices. You are highly discouraged from bringing any electronic device to this experiment (phones, computers, tablets, calculators, etc.).

End of Pre-Lab

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Part I: The Charge on the Dome

The first thing to understand about this Van de Graaff generator is that these devices are STOP not dangerous unless you have a pacemaker or other such electronic medical device. If you have an electronic medical implant or device, please alert your LAI immediately.

Now, even though the shocks you may receive aren’t dangerous, they can hurt a tiny bit. This is especially true if you get shocked through a finger since fingers are very sensitive. Getting shocked through your elbow feels a lot better. If at any point during the lab you are worried that you’ve built up a charge and that you’ll get shocked the next time you touch anything, it is highly recommended that you touch whatever that next thing is with your elbow. This is also good advice if you happen to own one of those couches where you’re always getting shocked after you watch some TV.

Equipment

• Van de Graaff generator • Tape

1. Are You the Positive or Negative Type?

These experiments today can be a little finicky. With that in mind, always test your predictions at least twice. If your results are inconsistent or ambiguous, it is recommended that you consult your LAI or another lab group.

Do This: Cut a strip of tape that is about 6 inches (~15 cm) long. Fold about 1 cm of the tape over onto itself in order to make a non-tacky handle. Label this handle with a T. This is tape-T. Stick tape-T to the plastic box so that it’s hanging freely. Gently brush your fingers over the tape to remove any static electricity.

Do This: Repeat the previous Do This but label the tape with a U. This is tape-U. Figure 1: How to stick tape-T to tape-U. Do This: You are about to stick these two strips of tape together in a very particular fashion. Stick them together such that the tacky side of tape-T is in contact with the un-tacky side of tape-U. See Figure 1.

Do This: Now pull the two strips of tape apart. Affix each strip of tape to the plastic box such that most of the strip is hanging freely as shown in Figure 2. This time do not brush your fingers over the tape.

Figure 2: Let the charged strips of tape hang over the edge of the box.

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Read This: In the process of tearing the two strips of tape apart, you have given each a net charge! By conservation of charge, these two strips must be oppositely charged. You will figure out which one is negatively charged and which one is positively charged. In order to accomplish this, here’s something that will come in handy:

FACT: When you rub plastic against your hair, the plastic becomes negatively charged.

Read This: A couple of plastic objects that work well are a pen or a Wash U ID card. In place of hair, you can use wool or silk, but it’s not quite as reliable.

Read This: Other lab groups are great resources. Before you write your response to the upcoming Synthesis Question, it might not be a bad idea to check if your results match those of a nearby group.

Read This: You must try both types of interactions: attraction and repulsion. Observing and discussing only one interaction will not always lead you to a correct conclusion.

Synthesis Question 1 (20 Points): Determine the sign of the charge on tape-T, the sign of the charge on tape-U, and the sign of the charge on the charged dome. (You can fully charge the S1 dome by turning the crank three times. Make sure the machine is grounded. Ask your LAI if you are not sure how to do it.) Your response must include your procedure, your observations, physics that explains your observations, and the conclusions you draw. Current Read This: The Laboratory for Materials Physics Research, led by Professor Kelton, levitate small metallic spheres using electrostatic forces in order to study crystal formation within the spheres.

Research These are the same forces that caused your strips of tape to attract or repel other charged objects. See the lab website for a link to more details.

Part II: Getting the Wands Involved

Equipment

• Van de Graaff generator with wands • Tape

2. How Charges Move in Conductors and Insulators

The goal of these upcoming experiments is to better understand how charges move in conductors and insulators, particularly the concepts of grounding, charging by contact, and induced charges.

Read This: Make sure that the grounding wand is plugged into the Van de Graaff generator as instructed by your LAI. The wire coming from the wand should be connected to the red plug on the base of the generator. If you are having any problems with this connection, alert your LAI.

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Do This: Turn the crank of the Van de Graaff generator three times. Then touch the dome with the grounding wand.

Checkpoint 2.1: What did you observe when you brought the grounding wand toward the dome?

Checkpoint 2.2: Predict what will happen if you touch the dome of the Van de Graaff generator with your elbow. (Note: you will not turn the crank any more before you touch the dome.)

Do This: Test the prediction you made in Checkpoint 2.2.

Checkpoint 2.3: Was your prediction accurate? If not, discuss where your reasoning failed.

Do This: Turn the crank of the Van de Graaff generator three times. Then touch the dome with the ungrounded wand. (Not the grounding wand.)

Checkpoint 2.4: What did you observe when you brought the ungrounded wand toward the dome?

Checkpoint 2.5: Predict what will happen if you touch the dome of the Van de Graaff generator with your elbow. (Note: you will not turn the crank any more before you touch the dome.)

Do This: Test the prediction you made in Checkpoint 2.5.

Checkpoint 2.6: Was your prediction accurate? If not, discuss where your reasoning failed.

Read This: Now let’s get the tape back in the mix.

Checkpoint 2.7: Predict the results (i.e. the behavior of the strips of tape) of the following experiment: After charging the Van de Graaff generator, you touch the ungrounded wand to the dome. Then you move this wand toward each of the two dangling strips of tape, one at a time.

Do This: Just to be safe, recharge your pieces of tape and stick them back on the plastic box. Recharging the tape is an especially good idea if either strip touches the dome or the wands.

Do This: Put the prediction you made in Checkpoint 2.7 to the test. Remember to test your prediction twice. Recharge your tape in between trials.

Checkpoint 2.8: Was your prediction correct? If not, discuss where your reasoning failed.

Checkpoint 2.9: Predict the results (i.e. the behavior of the strips of tape) of the following experiment: After charging the Van de Graaff generator, you touch the grounding wand to the dome. Then you move this wand toward each of the two dangling strips of tape, one at a time.

Do This: Put the prediction you made in Checkpoint 2.9 to the test. Remember to test your prediction twice. Recharge your tape in between trials.

Checkpoint 2.10: Was your prediction correct? If not, discuss where your reasoning failed.

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Read This: By now you should be getting pretty comfortable with the way charges move in conductors and insulators, so here’s a tricky challenge.

Synthesis Question 2 (20 points): Devise and test a method for putting an excess negative charge on the ungrounded wand using the Van de Graaff generator in tandem with the

S2 grounding wand. Explain your procedure for negatively charging the ungrounded wand and explain why it works. Further, explain how you tested that your method was indeed successful. Include figures as you see fit.

Part III: Energy Considerations

Equipment

• Van de Graaff generator with wands

3. The Van de Graaff Generator as a Capacitor

There are many concepts that you learned last semester that are going to come back again and again during the spring. Energy is one such topic. There are all sorts of new places where we see energy changing from one form to another during second semester physics. The transformation of energy between different forms can be quite spectacular when using the Van de Graaff generator.

Do This: Charge the generator by turning the crank a few times.

Checkpoint 3.1: Where and in what form is energy stored before you charge the dome?

Checkpoint 3.2: Where and in what form is energy stored after the dome is charged?

Do This: Bring the grounding wand toward the dome of the generator.

Checkpoint 3.3: Describe what happens (what you see, hear, etc.).

Checkpoint 3.4: What happened to the energy stored in the generator when you brought the grounding wand near the dome? If the energy has changed forms, which form(s) has it taken?

Read This: Let’s check your response to Checkpoint 3.4 by doing a little math.

Read This: A device like your Van de Graaff generator that stores electrical potential energy is called a capacitor. The capacitance of a capacitor is a quantity that relates the charge stored on a capacitor, the potential difference between its plates (or the potential of a single plate), and the energy stored by the capacitor. A capacitor with capacitance � storing a charge � on plates with a potential difference ∆� (equivalent to V used in some textbooks) stores an amount of energy � given by

1 �! 1 1 � = = � ∆� ! = � ∆� 2 � 2 2

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(If the capacitor has a single plate, then ∆� is the potential of the plate relative to ground.)

The capacitance is a strictly geometric property, depending only on the shape and material of the capacitor. For an isolated conducting sphere such as the dome of your Van de Graaff generator, the capacitance is given by

� � = 4�� � = ! �

where �! is the permittivity of free space, � is Coulomb’s constant, which has a value of approximately 9×10! Nm!/�!, and � is the radius of the sphere. The dome has a radius of 13.8 cm. Be aware that this equation only gives the capacitance of an isolated sphere. For other geometries, like the parallel-plate capacitor, a different equation needs to be used.

Checkpoint 3.5: Estimate (do not use calculator) the capacitance of your Van de Graaff generator by treating it as an isolated conducting sphere.

Checkpoint 3.6: According to the manufacturer, the dome of your Van de Graaff generator reaches an electrical potential on the order of 100,000 V when it is fully charged. Approximately how much electrical potential energy is stored by the fully charged dome?

Checkpoint 3.7: Approximately how much excess charge is stored by the fully charged dome?

Checkpoint 3.8: If you ground the dome (as you did in the experiment), then all of the excess charge on the dome will flow to the earth, which itself can be modeled as an isolated conducting sphere. How much electrical potential energy is stored by the earth if it has an excess charge equal to your response to Checkpoint 3.7? (The radius of earth is approximately 6 x 106 m.)

Synthesis Question 3 (20 Points): Consider again the energy transformations that occur when the charged dome gets grounded. Write a response to a friend who says, “When the charged dome gets grounded, all of the electrical potential energy stored on the dome is transformed 3 S3 into electrical potential energy stored on the earth.” Show to your friend that his/her statement is wrong including some calculations to support your response. Make sure these calculations are part of a cohesive explanation. Finally, if the energy has in fact been transformed to other forms, based on your observations, suggest what form(s) the energy has taken. (You will not receive full credit unless your response reads like a response to your friend.)

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Part IV: Electric Potential

The Story

Electric lines around town are typically at electric potentials of about 4000 V. Downed lines are a serious danger that you should not approach! Why, then, can a bird safely perch on a power line?

Equipment

• Van de Graaff generator • Small fluorescent light bulb (found inside cardboard tube) • Black test lead with banana plug on one end and alligator clip on the other end

4. Fluorescent Light

Before we get back to birds, let’s consider how this room is lit. Looking upward, you will notice that the light is coming from a series of fluorescent light bulbs. In these systems, electrical energy (which originated in a power plant of some sort) has been converted into the light energy that eventually reaches your eye.

In order to light up a room, the two ends of a fluorescent bulb must be at different electrical potentials. This potential difference accelerates electrons, giving them kinetic energy that is used to create light. (Light is produced through an interesting chain of events that you will investigate a bit in this semester’s Spectra lab.)

Do This: Connect one end of the test lead to the red ground plug on the base of the generator and connect the other end, via an alligator clip, to one end of your small fluorescent bulb. Holding it by the glass tube, place the unconnected end of the fluorescent bulb very near (just a few millimeters away) but not touching the dome of the Van de Graaff generator.

Checkpoint 4.1: What do you observe when turning the crank with the grounded bulb held near the dome? (Hint: if nothing is happening, move the bulb closer to the dome)

Do This: Now connect one end of the light bulb to the dome of the generator via the test lead and alligator clip (there is a receptacle for the banana plug on the top of the dome). Plug the grounding wand back into the red plug on the base of the generator.

Read This: Don’t charge up the generator just yet! If things are connected correctly, there’s a good chance that whoever is holding the fluorescent bulb will get charged up as well. To avoid

STOP building up an amount of charge that might result in a painful (but harmless) shock, have your partner touch you in the elbow with the grounding wand once each time the crank makes a full revolution. Again, this process avoids the charge you might build up, but you need to pay attention to what happens to the bulb.

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Do This: Holding it by the glass tube, place the unconnected end of the fluorescent bulb very near (just a few millimeters away) but not touching the dome of the Van de Graaff generator. Turn the crank, keeping in mind the previous Read This.

Checkpoint 4.2: Pay attention to the bulb. Describe what you observe when you crank the wheel of the generator.

Checkpoint 4.3: Discuss your observations (Checkpoints 4.1 and 4.2) in terms of electrical potential. (If your observations were not different, consult your LAI or a nearby group.)

Synthesis Question 4 (20 points): Relate the experiments you have just done with the fluorescent light to a bird’s ability to stand on power lines safely. Include observations from your S4 experiments, and relate each case to an analogous situation involving a bird and power lines. A good discussion will correctly use the term “potential difference.” (Hint: a potential difference is a difference, so it can only exist between two different points)

Part V: Dielectric Breakdown

Equipment

• Van de Graaff generator with wands

5. Lil Lightnin’

You’ve probably seen some pretty fantastic little lightning bolts by now. Let’s investigate those in a little more detail.

Do This: Have one partner turn the crank at a gentle, constant rate. Have the other partner hold the grounding wand by the plastic handle a short distance (roughly 3cm) away from the surface of the dome. Observe approximately how many sparks you see over a period of 5 seconds.

Read This: The number of sparks observed over a unit of time (1 second) is a quantity that we will refer to as the "frequency of sparks".

Do This: Just as before, have one partner turn the crank at a constant rate. This time, have the other partner hold the wand further (roughly 6cm) away from the dome. Observe the frequency of sparks.

Do This: Again, have one partner turn the crank at a constant rate. This time, have the other partner hold the wand further (roughly 9cm) away from the dome. Observe the frequency of sparks.

Do This: One last time, have one partner turn the crank at a constant rate. This time, have the other partner hold the wand further (roughly 12cm) away from the dome. Observe the frequency of sparks. Organize the data into a data table.

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Checkpoint 5.1: What is the relationship that you observe between spark frequency and wand distance?

Checkpoint 5.2: What do you predict that you could observe about the frequency of sparks if the grounding wand were initially held close to the dome, and then slowly moved further away, with the crank being turned at a constant rate?

Checkpoint 5.3: Test your prediction.

Now, let’s be clear about what happens when you see one of those sparks. Sparks (and lightning bolts) are the result of a phenomenon known as dielectric breakdown. When the magnitude of the electric field in air exceeds a value of about 3 x 106 V/m, air turns into a conductor as electrons are ripped from the air molecules by the strong electric field. (This critical electric field is called the dielectric strength of air.) If the field is larger than the critical value in the entire region between two objects of different potential, there will be a path of ionized air which will briefly carry charge as a spark! We will learn more about why light is produced later in the semester.

Checkpoint 5.4: What is the equation for the magnitude of the electric field around a spherically symmetric charge distribution?

Read This: Keep in mind that as you turned the crank at a constant rate, new charge was added to the dome at an approximately constant rate.

Checkpoint 5.5: Consider the equation you identified in Checkpoint 5.4 as representing the electric field around the dome. In Checkpoint 5.3, when you turned the crank at a constant rate, and slowly moved the wand away from the dome, which quantities in the equation were held constant, and which ones were not?

Checkpoint 5.6: How do each of the nonconstant quantities identified in Checkpoint 5.5 affect the frequency of sparks? In other words, when you increase or decrease those quantities, does the frequency of sparks increase or decrease?

Synthesis Question 5 (20 points): When the crank is turned at a constant rate, how does the distance between the wand and the dome affect how frequently sparks occur? Explain why S5 with a logical argument using your observations and your response to Checkpoint 5.4.

References

[1] Jonnes, Jill. (2003). Empire of Light. Random House, USA.

[2] Hinterberger, F. (2005). “Electrostatic Accelerators”. CERN Accelerator School, The Netherlands.

[3] Posteberg, F., et al. (2011). “A New View on Interstellar Dust - High Fidelity Studies of Interstellar Dust Analogue Tracks in Stardust Flight Spare Aerogel”. Lunar and Planetary Science Conference, Houston, TX.

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