For a volume $V$ with surface $S$, state Gauss's Law relating the flux of $\mathbf{E}$ across $S$ to the total charge within $V$.

A uniformly charged sphere of radius $R$ has total charge $Q$.

(a) Find the electric field inside the sphere.

(b) Using the differential relation $d \mathbf{F}=\mathbf{E} d q$ between the force $d \mathbf{F}$ on a small charge $d q$ in an electric field $\mathbf{E}$, find the force on the top half of the sphere due to its bottom half. Express your answer in terms of $R$ and $Q$.