Physics 1BL Coulomb’s Law and Superposition Winter 2010

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Introduction In this lab you will work on the ideas of Coulomb’s Law, electric field, and the superposition of Coulomb forces. You will explore how the electrostatic force between charges depends on distance, and demonstrate the ideas of superposition with multiple charges. Finally, you can check your skills with Electric Field Hockey. __________________________________________________________________________ Pre-lab Activity: Read Serway & Faughn 15.3, 15.4 & 15.8

1) A Van de Graaff generator is charged so that the electric field exerted at its top surface is 1.2 x 106 N/C directed upwards. Find (a) the electric force exerted on a Styrofoam peanut (q = +0.25 µC) released at its surface, (b) the gravitational force on the peanut, and (c) its net acceleration. (assume g = 10 m/s2; mpeanut= 0.75 grams).

2) Two charged balls, one with a charge of +5.0 µC and the other with a charge of +2.4 µC, are placed a distance d = 15.0 cm apart from each other and rigidly held in place. A third ball with a charge of +2.0 µC is dangled from a string between the two charged balls such that it remains in equilibrium. Calculate the distance the third charged ball is from to the +2.4 µC charge.

3) Three charges are arranged in a square (along with point P) with sides equal to 2.0 cm as in Figure 1. Calculate the electric field (magnitude and direction) at point P due to the three charges. Next, calculate the force (magnitude and direction) on a +0.50 µC charge placed at point P.

+4.0 µC –5.0 µC

2.0 cm Figure 1

P +3.0 µC

Physics 1BL Coulomb’s Law and Superposition Winter 2010

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The two balls before charging LAB WORK: A: Group Activity In this white board activity, imagine that you are given two non-conducting balls, of equal masses, each attached to an insulating string. You also have a scale to measure weight, a ruler, and a charging mechanism. A1. The balls hang vertically side by side, as shown, when

they are not charged. Predict and sketch what happens when you charge both balls equally (charges are equal in both magnitude and sign). Assume that the excess charge is distributed uniformly over each ball’s surface.

A2. Sketch what happens if you give a double dose of the same sign charge to the right ball? (e.g., Q on the left and 2Q on the right).

A3. Draw a force diagram for the left ball in situation A2. A4. Write an expression for the electrostatic force and the charge on the left ball. A5. Look at each variable in your expression for charge. Which quantities can be measured

with the equipment at hand? Which quantities cannot be measured? Can you express the quantities that cannot be measured in terms of measurable quantities?

A6. Write an expression for the charge on one of the balls in terms of measurable quantities only.

B. Using Coulomb’s Law

B1. In this exercise we will substitute balloons for the two balls. You will need to inflate two identical balloons to the same size. Start with both of the balloons uncharged. Rub one of the balloons against your clothing, rotating it several times so that you get a fairly even distribution of charges over its surface. (The technical term for the amount of charge on a surface is surface charge density. You are trying to achieve a uniform surface charge density on the balloons. Surface charge density is measured in coulombs/square meter. You will use this term later in class). Leave the other balloon uncharged. Draw a picture of how the charge is distributed on the charged balloon. Remember, there are both positive and negative charges present, but there will be slightly more of one type of charge than the other. Use “top” and “bottom” tape strips as you did last week to determine which type of charge the balloon has in excess.

B2. Now charge the second balloon in the same way, and ‘refresh’ the charge on the first. Suspend both balloons from cotton threads as shown in Figure 2. How can you approximately measure the angles between the threads and vertical? Do you think the balloons have equal charges? How could you observe if their charges are different in sign or in magnitude?

Physics 1BL Coulomb’s Law and Superposition Winter 2010

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B3. Measure the separation distance r and the angle θ for your configuration. Assume that the “center” of the charge distribution for each balloon is the center of the balloon. (When you consider mass or weight you can define a center of mass, or center of gravity. Similarly, for a distribution of charges you can have a center of charge. For a uniform distribution of surface charge on a sphere this will be at the center of the sphere). Using the equation derived for the white board activity, calculate the electrostatic force (in Newtons) on each balloon and the charge (in coulombs) on each balloon.

B4. Put your charge value on the class white board for comparison with other groups in the lab. Are the values similar? What might limit the amount of charge you can store on a balloon?

C. Exploring Superposition of Coulomb Forces

C1. Suspend a foil covered ping-pong ball by a thread from a rod. Charge the ball using PVC pipe and wool. Explore what happens when you bring the PVC pipe near, but not touching, the charged ball.

C2. Find a second PVC pipe. Charge the ball as for C1, but rub both PVC pipes so each pipe is charged. Explore what happens when you bring both the PVC pipes near, but not touching, the charged ball. Keep both pipes on the same side of the ball.

C3. Repeat C2 but with the pipes on opposite sides of the charged ball. Do the pipes have the same magnitude of charge?

C4. What forces are acting on the ball in C3? Draw a force diagram. C5. How does the principle of superposition help to explain the phenomena you are

observing?

D. The Van de Graaff Generator: CAUTION: Please remove pagers, cell phones and watches before approaching the generator. These items can be damaged by electrostatic discharges. Do not attempt this if you have a pace-maker.

Note: To discharge the Van de Graaff generator, hold the grounding rod against the metal sphere, turn off the generator, and then take the grounding rod away from the metal sphere. Always discharge the metal sphere and turn off the generator when you complete each procedure. Review Chapter 15.8 (P 485) from your text for information on how the Van De Graaff generator accumulates charge.

Physics 1BL Coulomb’s Law and Superposition Winter 2010

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D1. With the Van de Graaff generator turned off, place a stack of pie tins on the metal sphere. Turn the generator on and observe what happens. Briefly describe your observations. What do you think could have caused what you observed? When you are finished, turn off the generator and discharge it.

D2. Make sure the generator is switched off and discharged. Fill the small metal dish with Styrofoam peanuts. Place the dish on top of the metal sphere and turn on the generator. Briefly describe what you observe. What do you think caused this to happen? If you make a mess, pick up before you leave the lab.

D3. With the generator turned off and discharged, stand on the Styrofoam block (be sure your feet do not hang over the edge!), and put one hand firmly on the generator. Turn on the generator. Describe what you (or your lab partners) see and feel.

D4. Have your TA demonstrate how one can draw a spark from the generator to one’s hand. Try it if you wish. How long a spark can you get?

E. Electric Hockey:

You have access on the lab computers to “Electric Hockey”. This is a hybrid between a game and educational software. For personal use you can download it for free from the University of Colorado: http://phet.colorado.edu/simulations/sims.php?sim=Electric_Field_Hockey. Click the “Run Now!” button to start the simulation. It may take a while for it to start. If that doesn’t work try clicking the “Run Offline” button. You will find other good physics simulations at the same phet.colorado.edu website. Using “Electric Hockey”, try the “practice” level first, turn on both the “trace” and “field” options. Observe how the force on the “test” particle changes as you install and move other charges around nearby. When you hit “start”, you should be able to see the motion of your charged particle under the influence of charges you have selected. Can you make a closed, repeating pattern? What conditions are necessary for a repeating pattern? (Note: if the particle goes off the screen, sometimes it comes back later. You should get a rough idea under what conditions it will return and when it will be gone forever). Still in “practice” mode, try the arrangement of charges from pre-lab question 3. Is the initial motion of P in agreement with the answer you gave for this question?

Also try the “difficulty 1” game in which you try to score a goal. Try to use the minimum number of charges to steer your particle to the goal.

Conclusion:

1) Please do a write up conclusion on what the TAs specified in class.