# PHYS 2212 Module 4 Class Activities

## Capacitance

### I. The electric field near conducting plates

A. A small portion near the center of a large thin conducting plate is shown magnified at right. The portion shown has a net charge Q1 and each side has an area A1.

1. Write an expression for the charge density on each side of the conducting plate.

B. Use the principle of superposition to determine the electric field inside the conductor (if you have not done so already).

C. Use the principle of superposition to determine the electric field on each side of the plate.

1. Does the charge on the right surface contribute to the electric field to the left of the plate (even though metal separates the two regions)? Explain.

D. Consider instead a portion near the center of a large sheet of charge. Like the plate in part A , the portion of the sheet has a net charge Q1 and area A1.

1. How does the charge density on this sheet compare to the charge density on each side of the plate above? Explain.
2. How does the electric field on one side of the sheet of charge compare to the electric field on the same side of the charged plate? Explain.

E. A second plate with the same magnitude charge as the first, but opposite sign, is now held near the first. The plates are large enough and close enough together that fringing effects near the edges can be ignored.

The diagrams below show various distributions of charge on the two plates. Decide which arrangement is physically correct. Explain.

### II. Parallel plates and capacitance

Two very large thin conducting plates are a distance D apart. The surface area of the face of each plate is A0. A side view of a small portion near the center of the plates is shown.

A. The inner surface of one plate has a uniform charge density of ; the other, . The charge density on the outer surface of each plate is zero.

1. At each labeled point, draw vectors to represent the electric field at that point due to each charged plate.
2. Write expressions for the following quantities in terms of the given variables:
• the electric field at points I , 2, 3, and 4
• the potential difference between the plates

3. The right plate is moved to the left as shown. Both plates are kept insulated. Describe how each of the following quantities will change (if at all). Explain.

• the charge density on each plate
• the electric field both outside and between the plates
• the potential difference between the plates

4. Write expressions for the following quantities in terms of and d (the new distance between the plates).

• the magnitude of the electric field between the plates
• the potential difference between the plates

5. Find (the ratio of the net charge on one plate to the potential difference between the plates).

• How, if at all, would this ratio change if the charge densities on the plates were and ?

Check in with an LA or instructor before proceeding.

B. Suppose the plates are discharged, then held a distance D apart and connected to a battery. (Ignore the fringing fields near the plate edges.)

1. Write expressions for the following quantities in terms of the given variables. Explain your reasoning in each case.
• the potential difference between the plates
• the electric field at points 1, 2, 3, and 4
• the charge density on each plate

2. The right plate is moved to the left. Describe how each of the following quantities changes (if at all). Explain.

• the potential difference between the plates
• the electric field both outside and between the plates
• the charge density on each plate
1. Write expressions for the following quantities in terms of V0 and d (the new distance between the plates).
• the magnitude of the electric field between the plates
• the charge density on each plate
2. Find (the ratio of the net charge on one plate to the potential difference between the plates).
• H0w, if at all, would this ratio change if the voltage of the battery was 2V0?

Check in with an LA or instructor before proceeding.

C. Compare the ratio that you calculated for two insulated plates (part A) to the same ratio for two plates connected to a battery (part B).

1. Does the ratio depend on whether or not the plates are connected to a battery?
2. Does the ratio depend on the distance between the plates?

The potential difference between two isolated conductors depends on their net charges and their physical arrangement. If the conductors have charge +Q and -Q, the ratio is called the capacitance (C) of the particular arrangement of conductors.

D. For the following cases, state whether each of the quantities q, , E, , and C changes or remains fixed:

1. two insulated conducting plates are moved farther apart
2. two conducting plates connected to a battery are moved farther apart