Two points $P$ and $Q$ are maintained at the potentials of $10 \mathrm{V}$ and $-4 \mathrm{V},$ respectively. The work done in moving $100$ electrons from $P$ to $Q$ is

Statement $1$: For a charged particle moving from point $P$ to point $Q,$ the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q.$

Statement $2$: The net work done by a conservative force on an object moving along a closed loop is zero.

This questions 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 $R$ has a uniformly positive charge density $\rho .$ As a result of this uniform charge distribution there is a finite value of the electric potential at the centre of the sphere, at the surface of the sphere and also at a point outside the sphere. The electric potential at infinity is zero.

Statement $1$: When a charge is taken from the centre to the surface of the sphere its potential energy changes by $\frac{q\rho }{3{\epsilon }_0}$
Statement $2$: The electric field at a distance $r(r<R)$ from the centre of the sphere is $\frac{\rho r}{3{\epsilon }_0}$