Question

Conceptual Questions :
If the total charge inside a closed surface is known but the distribution of the charge is unspecified, can you use Gauss’s law to find the electric field? Explain.

Answer 1

Gauss's law cannot be used to find the electric field at different points on a surface if the field is not constant over that surface. If the symmetry of an electric field allows us to say that $\int E\cos \theta dA=E\int \cos \theta dA$, where $E$ is an unknown constant on the surface, then we can use Gauss's law. When electric field is a general unknown function $E(x,y,z)$ there can be no such simplification.