Question

State And Prove Gauss Theorem In Electrostatics

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Answer 1

$\maltese$ $\bold\red{\underline{EXPLAINATION:}}$ $\maltese$

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 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

Therefore,

σ = 1 / 4πɛo q / r² × 4π r²

σ = q / ɛo

Hence proved!!