Gauss theorem concept and derivation | class 12 Physics | advguruji

Statement :

The net electric flux through any closed surface is equal to 1/εο times the charge enclosed by the surface.

             Φ = q/εο

where, q = charge enclosed by the surface

PROOF

consider, a positive point charge q which is enclosed by an imaginary spherical shell of radius r with 'q' at the centre. ds is a very very small area element of the shell.

As we know, the electric field of a positive charge is always radially outward.

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Now, small electric flux through 'ds' is -

But, E = q/(4πεο.r²)

Therefore,

dΦ = [ q/(4πεο.r²) ].ds

Now,

Net electric flux through the whole spherical surface is -

(Integrating both sides and taking limits)

Question

Find the value of x in the figure if the net flux through the Gaussian surface is '1/2εο' Nm²/C.

For "electric field near an uniformly charged infinite sheet Notes"

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