Question

Two uniformly charged conducting plates are parallel to each other. They each have area A. Plate #1 has a positive charge Q while plate #2 has a charge −2 Q. Find the magnitude of the electric field at a point P in the gap. Assume that the separation between the plates is very small compared to the dimensions of the plates.

Answer 1

Answer:

$E = \frac{3Q}{2A\epsilon_0}$

Explanation:

By Gauss Law for electric field:

$E = \frac{\sigma}{2\epsilon_0}$

Where $\sigma$ is the charge density Q/A. Since we have 2 parallel  plates with different charge, the electric field at point P in the gap would be the sum of 2 field

$E = E_1 + E_2$

$E = \frac{Q}{2A\epsilon_0} + \frac{2Q}{2A\epsilon_0}$

$E = \frac{3Q}{2A\epsilon_0}$