Obtain the expression of electric field by thin spherical shell with uniform charge distribution at a point inside it.

Explanation

As shown in figure, surface charge density on spherical shell of radius R is `sigma`

The point P is inside the shell. The Gaussian surface is a sphere through P centered at O of radius r.
The flux through the Gaussian surface, calculated as before is `E xx 4pir^(2)`. In this case, the Gaussian surface encloses no charge.
Gauss.s law gives,
`E xx 4pir^(2) =0 , (therefore q/epsilon_(0) =0 "as" q=0)`
`therefore E =0, (r lt R)`
Thus, the field due to a uniformly charged thin shell is zero at all points inside the shell.