Question

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

• A. $\frac{\sigma }{\epsilon _{0}}$
• B. $\frac{\sigma }{2 \epsilon _{0}}$
• C. $\frac{3 \sigma }{2 \epsilon _{0}}$
• D. $\frac{3 \sigma }{\epsilon _{0}}$

Answer 1

Answer: (C)

The electric charge densities are $\sigma , \, -2\sigma $ and $4\sigma $ respectively.
Hence, electric field at point $P$ is given by
$E_{P}=\frac{\sigma }{2 \epsilon _{0}}+\frac{- 2 \sigma }{2 \epsilon _{0}}+\frac{4 \sigma }{2 \epsilon _{0}}$
$=\frac{\sigma - 2 \sigma + 4 \sigma }{2 \epsilon _{0}}$
$=\frac{3 \sigma }{2 \epsilon _{0}}$