Derivation of Gauss’s Theorem by Using Coulomb’s Law:
According to definition of electric flux,
\(\phi_{E}=\oint_{S} \vec{E} \overrightarrow{d s}=\oint_{S} E d s \cos \theta\)
The intensity of electric field \(|\vec{E}|\) at same distance from charge q remains constant and for spherical surface θ = 0°.
According to Coulomb’s law. intensity of electric field at distance r from charge q.
This is Gauss’s theorem.
