By constructing a spherical Gaussian surface centred on an infinite line of charge and by calculating the flux through the sphere we will show that the Gauss’ law is satisfied.

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Electric field at a distance r from an infinite line of charge of linear charge density is

,

and its direction is normal to the line.

We consider a spherical Gaussian surface of radius R centred on the line as shown in the figure. Flux through Gaussian surface of area

will be

Therefore,

.

And charge contained inside the sphere is .

Therefore, we have

,

and Gauss’ law is verified.