Question

Two large metal sheets having surface charge density $+\sigma/2$ and $-\sigma/2$ are kept parallel to each other at a small separation distance d. The electric field at any point in the region between the plates is

• A. $\sigma/2\epsilon_0$
• B. $\sigma/\epsilon_0$
• C. $\sigma/4\epsilon_0$
• D. $2\sigma/\epsilon_0$

Answer 1

Answer: (A)

$\sigma/2\epsilon_0$

Answer 2

The electric field due to a single infinite sheet with surface charge density $\rho_s$ is $E = \frac{|\rho_s|}{2\epsilon_0}$.

For the positive sheet ($+\sigma/2$), the field is $E_1 = \frac{\sigma/2}{2\epsilon_0} = \frac{\sigma}{4\epsilon_0}$, directed away from it.

For the negative sheet ($-\sigma/2$), the field is $E_2 = \frac{|-\sigma/2|}{2\epsilon_0} = \frac{\sigma}{4\epsilon_0}$, directed towards it.

Between the plates, both fields point in the same direction.

Total electric field $E_{total} = E_1 + E_2 = \frac{\sigma}{4\epsilon_0} + \frac{\sigma}{4\epsilon_0} = \frac{\sigma}{2\epsilon_0}$.