A spherical conducting shell of inner radius `r_(1)` and outer radius `r_(2)` has a charge Q.
a. A charge 'q' is placed at the centre of the shell. What is the surface charge density on the inner and outer of the shell?
b. Is the electric field inside a cavity (with not charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

Explanation

a. `(-q)/(4pi r_(1)^(2)), (Q+q)/(4pi r_(2)^(2))`
b. Yes. By Gauss law