# What is the physical interpretation of the average charge on a sphere due to a piont charge?

This question is motivated by Problem 3.4 in Griffiths' book on Electrodynamics.

This problem asks to calculate the average electric field on a sphere, due to charges inside the sphere and outside the sphere. For simplicity, let's just considering a point charge $$q$$ with field $$\mathbf{E}=\frac{1}{4\pi\epsilon_0}\left(\frac{q}{r^2} \right)\widehat{\mathbf{r}}.$$

If the charge is inside the sphere, then we have $$\mathbf{E}_{\mathrm{avg}}=\frac{1}{4\pi\epsilon_0}\left(\frac{q}{r^2} \right)\widehat{\mathbf{r}},$$ while if the charge is outside then we have $$\mathbf{E}_{\mathrm{avg}}=\mathbf{0}.$$

I understand the mathematical derivation of these results, but am having trouble coming up with a physical interpretation. The first result (outside the sphere) is elegant, but I cannot see why it should be true physically. I am also unable to come up with a physical interpretation of the second result, and a pointer in the right direction would be greatly appreciated.