Question

Surface density of charge on a sphere of radius $R$ in terms of electricity intensity $E$ at a distance $r$ in free space is ________.

(${ϵ}_0$= permittivity of free space)

• A. ${ϵ}_{0}E{\left(\frac{R}{r}\right)}^2$
• B. $\frac{{ϵ}_{0}ER}{r^2}$
• C. ${ϵ}_{0}E{\left(\frac{r}{R}\right)}^2$
• D. $\frac{{ϵ}_{0}Er}{R^2}$

Answer 1

The correct option is C ${ϵ}_{0}E{\left(\frac{r}{R}\right)}^2$

At distances greater than the radius from the center, the electric field due to a charged sphere is same as that of a point charge of same magnitude:

$E=\frac{Q}{4\pi {ϵ}_0{r}^2}$

Now, total charge and surface charge density are related by:

$Q=4\pi R^2\sigma$

This gives:

$\sigma ={ϵ}_{0}E(\frac{r}{R}{)}^2$