Experiment 33: Electric Field

October 2013

Purpose The purpose of this experiment is to: (1) To map the equipotential lines and construct electric field lines between two charged objects. (2) To understand the relationship between the electric potential and electric field strength.

Apparatus electric field mapping board, u-shaped mapping probe, two field plates and two stencils; power supply, digital multi-meter and connecting wires, white paper, masking tape, ruler

Theory Electric Field An electric field exists in the space around a charged object. It exerts a force on charged particles in the field. The magnitude of the electric field E is given by: E = F / q, where q is the magnitude of an infinitesimal test charge and F is the electric force felt by the test charge due to the field. The direction of the electric field is the direction that a positive charge would move due to the field.

Electric Potential Energy If a charge is moved by the force due to an electric field, work is done by the electric field. Electric potential energy represents the work done by the field when the charge is moved. The change in electric potential is equal to the negative of the work done by the electric field in moving the charge: ∆V = - E ∆d

An equipotential line is a line along which the potential is a constant; the potential difference between any two points on the line is zero. No work is required to move a charge at a constant speed along an equipotential line. Since no work is done when moving along the equipotentials, the field must be perpendicular to the equipotential lines.

We can draw Electric Field Lines to represent the electric field as follows: The direction of the electric field is tangent to the electric field lines at each point. Electric field lines start on positive charges and end on negative charges. Electric field lines are always perpendicular to the equipotential lines. No two field lines can cross each other.

The drawings below represent the Equipotential Lines (purple) and the Electric Field Lines (pink) of two different configurations. The drawing on the left represents the equipotentials and the field lines between two parallel plates. The drawing on the right represents the equipotentials and the field lines between two point charges. Notice that the electric field lines are perpendicular to the equipotential lines at every point and the electric field lines go from positive to negative charges.

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The electric field strength at a point is the potential difference ∆V between two nearby points which lie along a line in the direction of the electric field divided by the distance between the two points. E = ∆V / ∆d (1)

Procedure Part I: Parallel Plates 1. Flip the electric field mapping board over. Attach the parallel plates board with the silvery conducting side facing outward to the underside of the mapping board using the two plastic- headed thumb screws. (Figure 1) Turn the field mapping board over so the parallel plate will be underneath.

2. Attach a sheet of white paper to the top surface of the board. Tape down the four corners with masking tape to prevent the paper from moving.

3. Position the parallel plates stencil over the positioning pins. (Figure 2) Trace ONLY the parallel plate outlines onto the Figure 1 blank sheet of paper and remove the stencil. Label the “+” and “–” sides of the plates.

4. Connect the “+” terminal of the power supply to the “+” terminal of the board, and the “–” terminal of the power supply to the “–” terminal of the board with two long wires. - +

5. Take two more wires and connect the “com” port of the multimeter to the “–” terminal of the board, and the “VΩmA” port of the multi-meter to the “+” terminal of the board. (These wires will be connected on top of the first wires.) Turn the dial on the multi-meter to the 20V DC setting.

6. Turn on the power supply and adjust the voltage output to be 10 Volts. Figure 2

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7. Carefully slide the U-shaped probe over the lower edge of the mapping board with the ball end on the bottom.

8. Disconnect the “VΩmA” port of the multi-meter from the “+” terminal of the board and connect it to the top of the U- shaped probe. (Figure 3)

9. Do not squeezes the probe but move it left and right, up and down, and notice how the voltage changes.

Important: DO NOT squeeze the probe against the board when you are moving it to search for equipotential points. Holding the probe tightly closed while you slide it causes the electrode plates to wear out. Figure 3

10. Move the probe around until you find a point at 2 V and mark the point. Repeat this procedure many times until you can see the 2 V equipotential line clearly. Don’t forget to draw some points beyond the parallel plates. Connect the equipotential points with a smooth curve to show the equipotential line. Label the line.

11. Repeat step 10 for the 4 V, 5 V, 6 V, and 8 V equipotential lines. Label each line.

12. Draw 7 approximately equally spaced continuous dashed lines perpendicularly to the equipotential lines from one plate to the other. Show the direction of the electric field lines with arrows on the lines (remember the electric field lines are perpendicular to the equipotential lines and the direction of the electric field is the direction from the positive plate to the negative plate that a positive charge would move due to the field). DO NOT REMOVE THE PAPER YET!

13. Ask your lab instructor to mark 3 points on your paper along the electric field lines. Label them A, B, and C. Choose two points 0.5 cm on either side of A along the electric field line. Record the electric potential at these two points. Measure and record the distance ∆d between the two points. (You will use this data to calculate the magnitude of the electric field strength at these points in your lab report using Equation 1.)

14. Do the same for points B and C.

15. Remove the parallel plates and your drawing from the mapping board.

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Part II: Dipole Plate (Two Point Charges) 16. Attach the dipole plate to the mapping board as described in (1) and (2) above. (Figure 4)

17. Attach a blank sheet of paper to the mapping board and tape the paper to the mapping board as before. Use the dipole stencil to trace only the two dipole circles onto the paper. (Figure 5) Label the “+” and “–” circles.

18. Repeat steps 4 through 12 from Part I but find equipotential

lines for 3 V 4 V, 5 V, 6 V, and 7 V. Figure 4

19. Draw 7 equally spaced continuous dashed lines perpendicularly to the equipotential lines and indicate the direction of the electric field lines. This field will be very different from the field in Part I.

21. Please turn off the multimeter when you are done.

Figure 5 Lab Report

Part I 1. Include your drawing from Part I.

2. Use equation (1) to calculate the electric field strength EA, EB and EC at points A,B, and C .

Part II 3. Include your drawing from Part II.

Answer the following questions: 4. If a volt is a joule/coulomb, show that a newton/coulomb and a volt/meter are equivalent.

5. Are the 4 V, 5 V, 6 V equipotential lines between the two parallel plates evenly spaced? Explain why or why not.

6. Is it possible for two different equipotential lines to cross? Explain.

7. Sketch the electric field lines between two positively charged small spheres placed a short distance from each other.