Question

Show, by integrating Coulomb’s Law, that the field anywhere inside of a spherical shell with uniform surface-charge distribution, is zero. You are not allowed to make use of Gauss’ Theorem. Hint: start by showing that the field anywhere along an axis of the sphere is zero. Then, reason that any point within the sphere can be considered to be along a symmetry axis. Warning: be careful, once you do the integral, to make sure you take consistent signs for square roots.

Answer 1