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# Sate and prove coulomb inverse square law using gauss theorem

Murali Ramalingam
14 Points
one month 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*$r^2^{}$.
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
${\oint }$E dA

Since E is constant, we can just write E*4*pi*$r^2^{}$=q/$\epsilon$.

Since pi,q, epsilon are constant in this case, E is inversely proportional to $r^2^{}$, and therefore so is force.
Hence proved.