Question

Two thick plates having same charges (same charge density $\sigma$) are placed side by side. Consider the case of infinite plate. Find the difference between the electric field present between the plate and remaining space of the plate, ($\epsilon$=permittivity)

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

Answer 1

The correct option is A $\frac{\sigma }{\epsilon }$

The left plate produces a field $\left(\frac{\sigma }{{2ϵ}_0}\right)$ which points away from it to the left in the region $\left(i\right)$ and to the right in region $\left(ii\right)$ and $\left(iii\right)$. The right plate being negatively charged, produces a field $\left(\frac{\sigma }{{2ϵ}_0}\right)$ which points towards it to the right in regions $\left(i\right)$ and $\left(ii\right)$ and to the left in the region $\left(iii\right)$. The $2$ fields cancel in region $\left(i\right)$ and $\left(iii\right);$ they add in region $\left(ii\right).$ Thus the field between the plates is $\frac{\sigma }{{\epsilon }_0}$ and elsewhere, $0.$