Question

Three non-conducting large parallel plates have surface charge densities $\sigma ,-2\sigma$ and $4\sigma$ respectively as shown in figure. The electric field at the point $P$ is

• A. $\frac{\sigma }{{ϵ}_0}$
• B. $\frac{\sigma }{2{ϵ}_0}$
• C. $\frac{3\sigma }{2{ϵ}_0}$
• D. $\frac{3\sigma }{{ϵ}_0}$

Answer 1

The correct option is C $\frac{3\sigma }{2{ϵ}_0}$

The electric charge densities are $\sigma ,-2\sigma$ and $4\sigma$ respectively.
Hence, electric field at point $P$ is given by
$E_P=\frac{\sigma }{2{ϵ}_0}+\frac{-2\sigma }{2{ϵ}_0}+\frac{4\sigma }{2{ϵ}_0}$
$=\frac{\sigma -2\sigma +4\sigma }{2{ϵ}_0}$
$=\frac{3\sigma }{2{ϵ}_0}$