CBSE Class 12-science Answered
Deduce Coulomb's law from Gauss theorum.
Asked by Aarushi Srivastava | 11 May, 2022, 08:19: PM
Expert Answer
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)
.....................(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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