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Deduce Coulomb's law from Gauss theorum.
Asked by Aarushi Srivastava | 11 May, 2022, 08:19: PM
Gauss theorem states that total electric flux over a closed surface equals enclosed charge
divided by permittivity of enclosed medium.

Let us consider a sphere of radius R has charge at centre of sphere.

Then by Gauss theorem ,    .....................(1)
Where E is uniform electric field intensity over the surface of sphere , q is enclosed charge
and ε is permittivity of medium

Since Electric field intensity E is uniform over the surface of sphere ,
we can write the RHS of eqn.(1) as

= E × 4π R2 ........................(2)
where 4π R2 is surface area of sphere.

Using eqn.(1) and (2) , we write

E × 4π R2 = ( q / ε )

Hence Electric field E is written as

Above expression equals electric field at a distance R from a charge q.

Since electric field is force / unit charge , force experienced by a test charge q' at a distance R
from the given charge q  is written as

Above expression is Columbs law that gives electrical force between two charges q and q'
that are separated by a distance R

Answered by Thiyagarajan K | 11 May, 2022, 11:13: PM

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