Page 20 - Electrostatics-11

© GC Shiba
Applications of Gauss Theorem:

In actual practice, we can never have a point charge, rather we do have

charge bodies having different shapes. Coulomb law cannot be applied directly to
calculate the electric field having different shapes of charge bodies. In such
situations, Gauss theorem is applicable.

1) Electric intensity inside a charged conducting solid sphere
Consider a charge conducting sphere of radius R

having a charge +Q. We are interested to find the electric
intensity at point P inside a charged sphere. Let us draw a
concentric sphere of radius r through point P. This sphere is P

called a Gaussian sphere.
By symmetry, electric intensity would be the same at all
points on the surface of a Gaussian sphere. Electric flux from

the charged sphere is radially outward as shown in the
figure.
Now, electric flux passing through the gaussian surface is

ℎ
=
∈ 0

=E × A
or, E × A = 0 ( since no charge is enclosed by
gaussian surface)

E = 0
Hence, there is no electric field inside the charged sphere.

2) Electric intensity outside a charged conducting sphere

Consider a charge conducting sphere of radius R

having a charge +Q. We are interested to find the electric
intensity at point P outside a charged sphere. Let us draw
a concentric sphere of radius r through point P. This
sphere is called a Gaussian sphere.

By symmetry, electric intensity would be the same at all
points on the surface of a Gaussian sphere. Electric flux
from the charged sphere is radially outward as shown in

the figure.
Now, electric flux passing through the gaussian surface is

19 Electrostatics