Question

Find the electric field inside the shell at a distance $r$ from the centre.

• A. $E=0$
• B. $E=\frac{Q}{4\pi {ϵ}_0{r}^2}$
• C. $E=\frac{Q}{4\pi {ϵ}_0{a}^2}$
• D. $E=\frac{Q}{4\pi {ϵ}_0(a-r{)}^2}$

Answer 1

The correct option is A $E=0$

Given a thin spherical shell of radius ${}^{\prime }{a}^{\prime }$ and charge ${}^{\prime }{Q}^{\prime }$ distributed over its surface.

To find electric field at a point, inside a shell, which is at a distance $r$ from the center.

Let P be the point inside the shell at a distance $r(r<a)$ from center. Draw a gaussian surface (sphere) of radius $r$ with $0$ as a center.

According to Gauss' Theorem,

${\oint }_S\overrightarrow{E}.\overrightarrow{dS}=\frac{q}{{\epsilon }_0}$

Hence, gaussian surface encloses no charge i.e, $q=0$

So, ${\oint }_S\overrightarrow{E}.\overrightarrow{dS}=0$

or $E=0$