Question

Find the electric field at $-0.5d<z<0.5d$

• A. $E=0$
• B. $E=-\frac{\sigma }{ϵ}\hat{k}$
• C. $E=\frac{\sigma }{ϵ}\hat{k}$
• D. $E=-\frac{\sigma }{2ϵ}\hat{k}$

Answer 1

The correct option is B $E=-\frac{\sigma }{ϵ}\hat{k}$

Given two parallel infinite non-conducting planes lying in x-y plane separated by a distance $d$.

Each plane is uniformly charged with equal and opposite surface charge densities. So, ${\sigma }_1={\sigma }_2$

To find the electric field at $-0.5d<d<0.5d$,

The net electric field is given by

$E=\frac{-1}{2\epsilon }({\sigma }_1+{\sigma }_2)$

As ${\sigma }_1={\sigma }_2=\sigma$

$E=\frac{-2\sigma }{2\epsilon }=\frac{-\sigma }{\epsilon }\hat{k}$

$\hat{k}=$ unit vector normal to x-y plane.