Overview
Question
Show that the mean value of the electric field over the volume of a charge-free sphere is equal to the value of the field at its centre.
Please beware that this question regard electric field instead of electric potential.
I need an explicit formula proof of equality instead of qualitative explanation, you can refer to this proof for potential, in page 2 it is stated that (A related result is that the mean value of the electric field over the volume of a charge-free sphere is equal to the value of the field at its center.). And I need an explicit proof of that.
Reference:
https://www.physics.princeton.edu//~mcdonald/examp...