Question

Is the flux through a closed surface always zero?

Answer 1

1. Flux: according to Gauss's law, the flux across a closed surface is proportional to the net charge enclosed by the surface.
2. As a result, the electric flux through a closed surface is zero only when the net charge encompassed by it is zero.
3. The net electric flux is positive if the net charge contained is positive (outwards through the closed surface).
4. The net electric flux is negative if the net charge contained is negative (inwards through the closed surface).
5. The net flux is unaffected by the charge distribution within the closed surface or the presence of any charges outside it.
6. The net flux is independent of the closed surface's shape or form, whether spherical, cubical, or irregular, as well as its size.
7. As a result, the net flux will be independent of the field's uniform or non-uniform character.

Hence, if there is no source of the vector field in the volume enclosed by the surface, the flux of the vector field through the closed surface is always zero.