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Sate and prove coulomb inverse square law using gauss theorem

Sate and prove coulomb inverse square law using gauss theorem

Grade:12

1 Answers

Murali Ramalingam
14 Points
one year 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.

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