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Pre-Lab Preparation
Electric Potential, Equipotentials, and Electric Fields
(Due at the beginning of Lab) Directions: Read over the Electric Potential, Equipotential and Electric Field Lab, and then answer the following questions about the procedures. Question 1 In each of the figures 1(a), 1(b), and 1(c) a particle with a positive charge of magnitude q is moved a distance d in an electric field E. The magnitude of the charge, the distance d, and the strength of the electric field E are the same for all three figures. In figure 1a the path along which the particle is moved is parallel to the field, in figure 1(b) it is perpendicular to the field, and in figure 1(c) it makes a 45 ◦^ angle. In which figure is the work done by the field greatest? In which figure is it least? Explain your answers.
(a) B
A
(b)
A B
(c) (^) B
A
Question 2 If q = 5 × 10 −^9 C, E = 500N/C, and d = 0. 02 m (1 cm), calculate the amount of work done by the field on the particle in each of the figures.
Question 3 What is the change in the electrical potential energy in each of the figures? Be sure to properly indicate the sign (+ or −) of the change in potential energy.
Question 4 If E = 500 N/C and d = 0. 02 m (1 cm), calculate the electric potential difference between points A and B in each of the figures 1a, 1b, and 1c.
Question 5 Do you need to know the amount of charge, q, in order to answer question 1-4? Why or why not?
PHYS-204: Physics II Laboratory i
Question 6 In each of the figures, which point is at the higher electric potential, A or B? Explain.
Question 7 If the charge q were negative instead of positive, would your answers to question 1-6 stay the same?
Question 8 In physics I you learned that work is equal to force multiplied by displacement multiplied by the cosine of the angle between the force and the displacement:
You also know that the cosine of an angle has its maximum value (1) when the angle is 0. Use this to explain why the work done by an electric field is greatest when the displacement is parallel to the electric field.
Question 9 What is your answer to question 3.2 in the handout. Your answer to question 1 should help you to answer this question.
PHYS-204: Physics II Laboratory ii
Activity 1.1: Work Done on a Charge Traveling in a Uniform Electric
Field
Questions 1-1, through 1-7 should be answered before coming to class. Note these questions are in the pre-lab assignment.
Question 1.1 In each of the figures 1(a), 1(b), and 1(c) a particle with a positive charge of magnitude q is moved a distance d in an electric field E. The magnitude of the charge, the distance d, and the strength of the electric field E are the same for all three figures. In figure 1(a) the particle is moved parallel to the field, in figure 1(b) it is moved perpendicular to the field, and in figure 1(c) it is moved at a 45 ◦^ angle. In which figure is the work done by the field greatest? In which figure is it least? Explain your answers.
(a) B
A
(b)
A B
(c) (^) B
A
Question 1.2 If q = 5 × 10 −^9 C, E = 500 N/C, and d = 0. 02 m (1 cm), calculate the amount of work done by the field on the particle in each of the figures.
Question 1.3 What is the change in the electrical potential energy in each of the figures? Be sure to properly indicate the sign (+ or −) of the change in potential energy (Note: if the work done by the field is positive, then the field has used up energy to do this work, so the change in potential energy is negative.)
The electric potential difference is defined as the electrical potential energy difference per unit charge: ∆V = ∆PE/q The unit of electric potential difference is the Volt. One volt corresponds to 1 Joule/Coulomb.
Question 1.4 If E = 500 N/C and d = 0. 02 m (1 cm), calculate the electric potential difference between points A and B in each of the figures 1(a), 1(b), and 1(c).
Question 1.5 Do you need to know the amount of charge, q, in order to answer question 1-4? Why or why not?
Question 1.6 In each of the figures, which point is at the higher electric potential, A or B? Explain.
Question 1.7 If the charge q were negative instead of positive, would your answers to question 1-6 stay the same?
Measuring Potential Differences between two points in an electric field
In this activity you will measure the electric potential difference between between pairs of points in the electric field set up by pairs of conducting electrodes. To make these measurements you will need the following equipment:
- computer-based laboratory system.
- Experiment configuration files.
- 2 differential voltage sensors.
- water tray.
- electrodes mounted on a plastic grid.
- signal generator set to 60 cycle per second frequency.
- Two stiff wires to use as probes.
One of the sets of electrodes is a pair of bars mounted on a plastic grid as shown in Fig. 2 This arrangement simulates two parallel conducting plates. This is an important arrange- ment because it gives a uniform electric field in the region between the plates away from the ends.
Step 1: Place this set of electrodes in the tray, and pour in enough water to come up about 1/4th of an inch over the plastic grid.
Step 2: A clear plastic sheet has been cut out to go over these electrodes. Place it so that it lies flat on top of the plastic grid.
Step 9: Now measure the electrical potential difference from point B to point C, placing the negative probe on B, and the positive probe on C. Enter your measured value in Table 1. Continue by measuring the potential difference from C to D and enter your value into Table 1.
Question 1.8 How large is the total potential difference from point A to point D?
Question 1.9 How much work would be needed to move a particle with charge 2 × 10 −^6 C from point A to point B? B to C? C to D? Calculate the amounts of work, and enter them in Table 1.
Question 1.10 What would be the total work needed to move a particle with charge 2 × 10 −^6 C from point A to point D?
Total work A to D = Joules
Question 1.11 As the charged particle is moved from A to D, does its potential energy increase or decrease? By how much does the potential energy change?
Prediction 1.1 Suppose you were to move the charged particle from A to D along the straight line going from A through points E and F to D. Would the total amount of work be the same? Would you determine the same potential difference between points A and D?
Step 10: Check your predictions. Using the same technique as in steps 8 and 9, measure the potential difference from A to E, E to F, and F to D, and enter your measured values in Table 2.
Question 1.12 What is the total potential difference from A to D along the path through E and F. Does your measurement agree with your prediction? Because of the limits in
Potential Difference Work on 2 × 10 −^6 C charge. A to E E to F F to D
Table 2:
precision of the equipment, you should consider any discrepancies smaller than a few hundredths of a volt to be insignificant. Is it reasonable to expect that the amount of work needed to move a particle from A to D would be the same along any path? Why or why not?
Prediction 1.2 What is the electrical potential difference from B to E? Realize that the precision of the equipment is no better than about a tenth of a volt. Can you tell with certainty which point, B or E, has the higher potential?
Step 11: Check your prediction using the probes to measure the potential difference from B to E.
Question 1.13 Does your measurement agree with your prediction? Because of the lim- its in precision of the equipment, you should consider any reading smaller than a few hundredths of a volt to be a potential difference of 0.
Prediction 1.3 What is the electrical potential difference from C to F? Can you tell with certainty which point, C or F, has the higher potential?
Step 12: Check your prediction using the probes to measure the potential difference from C to F.
Question 2.2 Find some equipotential surfaces for the configuration of two charged parallel plates shown in Fig. 4, which consists of two charged metal plates placed parallel to each other. What is the shape of the equipotential surfaces?
Figure 4: Electric Field Between Parallel Conducting Plates
Question 2.3 Find some equipotential surfaces for the electric dipole charge configuration shown in Fig. 5
Question 2.4 In general, what is the relationship between the direction of the equipotential lines you have drawn (representing that part of the equipotential surface that lies in the plane of the paper) and the direction of the electric field lines?
Activity 2.2: Mapping out equipotentials experimentally
In this activity you will use the voltage probes to map out the equipotentials for the arrange- ments that you worked with in Activity 2.1. You will use the same equipment as in Activity
Step 1: One of the sets of electrodes has a post at the center, surrounded by a brass ring on a plastic grid as shown in Fig. 6. The center post simulates a point charge. We will think of the outer ring as being ”far away,” where it is customary to take the electrical potential to be zero (this is a slight approximation). Since the center post will be made positive, the electric field lines should be directed radially outward. Place this set of electrodes in the tray, and make sure the tray has enough water to come up about 1/4th of an inch over the plastic grid.
Figure 5: Electric Dipole Field
Figure 6: Coaxial Conducting Shells
Step 2: You will use the same file as in Activity 1.2, file L3A1 2 (Potential Differences).
Step 3: Clip the leads of each of the voltage sensors together to assure that the potential differences between the leads are zero. Click the zero button, and zero all sensors.
Step 4: Connect the positive (red) terminal of the signal generator to the center post, and connect the negative (black) terminal to the outer brass ring. This way the center post can be thought of as a positive point charge.
Step 5: Connect voltage sensor 2 with the negative lead of voltage sensor 2 to the outer ring, and the positive lead to the center post. Turn on the signal generator and adjust the frequency to 60 cycles per second. Then turn up the amplitude so that meter 2 reads 6 volts. Adjust the amplitude slowly enough that the meter reading can keep up.
Step 6: You will use voltage sensor 1 to locate points that have the same potential. Connect the negative lead of voltage sensor 1 to the outer ring. Clip the positive lead to the bare
sketches and your experimental plots? If there are differences, which plots are different, and how are they different?
Investigation 3:
Exploring Electric fields and electric field lines
In this investigation you will make measurements of the magnitude and direction of the electric fields produced by the arrangements of electrodes you have been using.
Activity 3.1: Sketches of electric field lines
Question 3.1 Recall what you answered for question 2.4 - that the equipotential lines are al- ways perpendicular to the electric field. Use this knowledge to draw a few of the electric field lines for the dipole, whose equipotentials are shone in Fig. 9. Draw field lines that start out downward from the positive charge at an angle of about 30 ◦^ from the vertical, and another at an angle 60 ◦^ from the line between the posts. Remember to make your field line curve in such a way that it intersects each equipotential at a right angle.
Figure 9: Dipole Equipotentials
Activity 3.2: Using the voltage probes to measure electric fields
In this activity you will learn a technique for measuring the electric field using a voltage sensor. You will then use this technique to map out some of the field lines of an electric dipole. Then you can tell if you correctly sketched these in activity 3-1.
Question 3.2 Suppose a particle with a positive charge were to move a certain distance, say
- 1 meter, in a uniform electric field. What direction should it move in order for the field to do the greatest amount of work, thereby producing the largest possible decrease in potential energy?
Your answer should help you understand that we can build an electric field probe by using two of our stiff wires mounted so that they are always separated by the same distance. Thus we can find the direction of the field by rotating the probes to get the largest possible potential difference. Once you have located the maximum potential difference, the direction of the field is from the positive toward the negative wire in your field probe. And when you have the field probe oriented in this way, the strength of the field is related to the potential difference measured by the sensor: E = ∆V /d where ∆V is the potential difference, and d is the distance between the tips of the stiff wires. To verify and make use of this idea, you will need the following equipment:
- computer-based laboratory system.
- experiment configuration files.
- Two differential voltage sensors.
- water tray.
- electrodes mounted on a plastic grid.
- signal generator set to 60 cycle per second frequency.
- An electric field probe consisting of two stiff wires mounted in a double hole stopper.
We shall first use the set of electrodes with two parallel bars to test the idea stated above, that as the two wires that are kept a fixed distance apart by the two hole stopper are rotated, they will give the maximum potential difference when they are oriented parallel to the field.
Step 1: Place the parallel bars electrode set in the water tray.
Figure 10: Two Parallel Conducting Bars
We know that the field in the middle of the region between the bars is uniform, and is di- rected straight across from one electrode toward the other, so it makes a good arrangement to test our idea. Make sure the tray has enough water to come up over the plastic grid about 1/4th of an inch.
Step 2: Open the experiment file L3A3 2 (Electric Field).
Step 3: Measure the distance between the ends of the two wires. The computer needs to know this distance because it uses the formula above that relates the electric field to the potential difference divided by the distance.
equipotential drawing for the two parallel bars. The vector should show the direction of the electric field at the point you have measured. Record the magnitude of the electric field next to your vector.
Question 3.5 Do you measurements show that the field is uniform in the region between the plates? If you found some points at which the field was different, how far from the ends were these points?
Extension 3-3: Measuring the field of a point charge and a dipole
Use the same technique you used in Activity 3.2 to find the field at a few points around the point charge (post and ring) and dipole (two posts) sets of electrodes. Record your measurements on the equipotential plots you have made for each of these arrangements by drawing vectors in the direction of the field. Record the magnitude of the field next to the vector.
Question 3.6 Are the electric field vectors you found always perpendicular to the equipoten- tials?
This laboratory exercise has been adapted from the references below.
References
[1] David R. Sokoloff, Priscilla W. Laws, Ronald K. Thornton, and et.al. Real Time Physics, Active Learning Laboratories, Module 3: Electric Circuits. John Wiley & Sons, Inc., New York, NY, 1st edition, 2004.
[2] Priscilla W. Laws. Workshop Physics Activity Guide, Module 4: Electricity and Magnetism. John Wiley & Sons, Inc., New York, NY, 1st edition, 2004.
