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Question

# Define electric flux. Apply Gauss' law to obtain an expression for the electric field intensity at a point due to an infinitely long uniformly charged straight wire. Draw the necessary diagram.

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Solution

## Electric flux is the measure of flow of the electric field through a given area. It is proportional to the number of electric field lines going through a normally perpendicular surface.For electric field →E passing through an area →A, the flux passing through it is →E.→A.According to Gauss' law, flux passing through a closed surface is proportional to the amount of charge in the enclosed volume.→E.→A=qencϵ0Let us take a cylindrical surface co-axial with the charge carrying straight wire as Gaussian surface.Enclosed charge in this volume as shown in figure, assuming linear charge density to be λ, is qenc=λLHence according to the Gauss' law,E(2πRL)=λLϵ0⟹E=λ2πϵ0R

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