( iii ) APPLICATION OF GAUSS'S LAW

( iii ) Electric Field due to a Uniformly Charged Thin Spherical Shell: -

Let s  = uniform surface charge density on a spherical shell of radius R. 

( a ) For points inside the shell: Since the charge enclosed in a spherical surface of radius r < R is

zero, the electric intensity is zero at all points inside it. ( b ) For points outside the shell: Applying Gauss’s Theorem to a spherical surface of radius r > R, 4 pr2 E( r ) = 4 pr2 s / e₀ 

where q is the total charge on the spherical shell. Thus for points outside the spherical shell, the entire charge of the spherical shell can be treated as concentrated at its centre.