I have a dipole sitting inside a charged sphere i.e. at the centre of the sphere. As far as I can see the force on the Dipole is zero because the external electric field on the dipole at $r=0$ is $0$. But what about the force due to the dipole on the sphere? We know that the electric field due to a dipole is given by $-\bar p\cdot \frac {\nabla \bar r}{r^3}$. I have come to the step (I don't know if I am right):
$$\frac{-3Q}{4\pi R^3} \int_{\partial V}\frac{\bar p\cdot\bar r}{r^3}.$$
Another case, If the sphere was a hollow sphere with the thickness $t$, what would be the force on the sphere due to this dipole?
