Problem

A sphere of charge of radius

R

carries a positive charge whose volume charge density depends only on the distance

r

from the ball's centre as

\rho=\rho_0\left(1-\frac{r}{R}\right)

, where

\rho_0

is a constant. Assume

\epsilon

as the permittivity of space. The magnitude of electric field as a function of the distance

r

inside the sphere is given by a.

E = \frac{\rho_0}{\epsilon} \left[ \frac{r}{3} - \frac{r^2}{4R} \right]

E = \frac{\rho_0}{\epsilon} \left[ \frac{r}{4} - \frac{r^2}{3R} \right]

E = \frac{\rho_0}{\epsilon} \left[ \frac{r}{3} + \frac{r^2}{4R} \right]

E = \frac{\rho_0}{\epsilon} \left[ \frac{r}{4} + \frac{r^2}{3R} \right]