JEE Main 2012 — Electrostatics Question with Solution

This question has statement $1$ and statement $2$ . Of the four choices given after the statements, choose the one that best describes the two statements. An insulating solid sphere of radius $\mathrm{R}$ has a uniformly positive charge density $\rho$. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero. Statement $1$: When a charge $q$ is taken from the centre to the surface of the sphere, its potential energy changes by $\frac{\mathrm{qp}}{3{\epsilon }_0}$ Statement $2$: The electric field at a distance $r(r<R)$ from the centre of the sphere is $\frac{\rho r}{3{\epsilon }_0}$