Murali Ramalingam
Last Activity: 4 Years ago
We consider the Gaussian surface to be a sphere with the point charge as center.
Since the idea is to find electric field at a point, say r meters away from the point charge, the radius of the sphere will also be r meters.
By symmetry, electric field will be equal through every point on the sphere.
The surface area of the sphere is 4*pi*

.
And net charge contained within the sphere is the point charge we started with, say q.
We now apply Gauss’ theorem.
Electric flux should be equal to

E dA
Since E is constant, we can just write E*4*pi*

=q/

.
Since pi,q, epsilon are constant in this case, E is inversely proportional to

, and therefore so is force.
Hence proved.