Question

A hollow spherical shell of radius r has a uniform charge density `sigma`. It is kept in a cube of edge 3r such that the centre of the cube coincides with the centre of the shell. Calculate the electric flux that comes out of a face of the cube.

Answer 1

For spherical shell, charge = q (say)
Radius = r
Charge density `=sigma=q/A=q/(4pi r^(2))`
`:.` Charge on spherical shell, `q=4pi r^(2) sigma`
Flux through one of the face of a cube,
`phi_(E)=1/6 q/epsi_(0)=1/6xx(4pi r^(2) sigma)/epsi_(0) =(2pi r^(2) sigma)/(3 epsi_(0))`