Question

Electric field intensity in free space at a distance '$r$' outside the charged conducting sphere of radius '$R$' in terms of surface charge density '$\sigma$' is :

• A. $\frac{\sigma }{{ϵ}_0}{\left[\frac{R}{r}\right]}^2$
• B. $\frac{{ϵ}_0}{\sigma }{\left[\frac{R}{r}\right]}^2$
• C. $\frac{R}{r}{\left[\frac{\sigma }{{ϵ}_0}\right]}^2$
• D. $\frac{R}{\sigma }{\left[\frac{r}{{ϵ}_0}\right]}^2$

Answer 1

The correct option is A $\frac{\sigma }{{ϵ}_0}{\left[\frac{R}{r}\right]}^2$

According to the Gauss law,

$\frac{q}{{ϵ}_0}=\overrightarrow{E}.\overrightarrow{A}$

Let us choose a sphere of radius $r$ concentric to the given sphere as Gaussian surface.

Hence $\frac{\sigma 4\pi R^2}{{ϵ}_0}=E\left(4\pi r^2\right)$

$⟹E=\frac{\sigma }{{ϵ}_0}[\frac{R}{r}{]}^2$