Chapter 5.5, Problem 2aT

The inner surface of one plate has a uniform charge density of $+{\sigma }_o;$ the other, $-{\sigma }_o$ . The charge density on the outer surface of each plate is zero.

1. At each labeled point, draw vectors lo 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 1, 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 expression for the following quantities in terms of ${\sigma }_o$ and d (the new distance between the plates).

• the magnitude of the electric field between the plates

• the potential differences between the plates

5. Find $\frac{Q}{\Delta V}$ (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 $+2{\sigma }_o$ and $-2{\sigma }_o$ ?