Applications of Gauss' Theorem:(Field Due to a Uniformly Charged Thin Spherical Shell)

Chapter-1|Electric Charges and Fields | NCERT 12th Physics:

Applications of Gauss' Theorem:

(III) Field Due to a Uniformly Charged Thin Spherical Shell:

Let σ be the uniform surface charge density of a thin spherical shell of radius R. The Gaussion surface will be a spherical surface centred at the centre of shell.

(a) At a point outside the Shell: (r>R)

Since E and n^ are in the same direction, So θ=0

Flux through the Gaussian surface-

(b) At the point on the surface of the Shell:(r=R)

(c) At the point inside the Shell: Since the charges inside the gaussian surface is zero.

Hence, Electric field due to a uniformly charged spherical shell is zero at all points inside the shell.