Question

Two infinite parallel metal planes, contain electric charges with charge densities $+\sigma$ and $-\sigma$ respectively and they are separated by a small distance in air. If the permittivity of air is ${ϵ}_0$, then the magnitude of the field between the two planes with its direction will be:

• A. $\sigma /{ϵ}_0$ towards the positively charge plane
• B. $\sigma /{ϵ}_0$ towards the negatively charged plane
• C. $\sigma /\left(2{ϵ}_0\right)$ towards the positively charged plane
• D. $0$ and towards any direction

Answer 1

The correct option is B $\sigma /{ϵ}_0$ towards the negatively charged plane

Direction of the electric field due to each plate is towards the negatively charged plate and contribution of each plate to the magnitude of field is same, i.e., $\frac{\sigma }{2{ϵ}_0}$.

The magnitude of the net field is therefore: $\frac{\sigma }{{ϵ}_0}$

So, option B is the correct answer.