Gauss’s Theorem Statement:
According to Gauss’s theorem the net-outward normal electric flux through any closed surface of any shape is equivalent to 1/ε0 times the total amount of charge contained within that surface.
Proof of Gauss’s Theorem Statement:
- Let the charge be = q
- Let us construct the Gaussian sphere of radius = r
Now, Consider, A surface or area ds having ds (vector)
Normal having the flux at ds:
Flux at ds:
d e = E (vector) d s (vector) cos θ
But , θ = 0
Therefore, Total flux:
C = f d Φ
E 4 π r2
σ = 1 / 4πɛo q / r2 × 4π r2
σ = q / ɛo
According to the Gauss law, the total flux linked with a closed surface is 1/ε0 times the charge enclosed by the closed surface.