Question

# State Gauss law in electrostatics. Using the law derive an expression for electric field due to a uniformly charged thin spherical shell at a point outside the shell.

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Solution

## Gauss Law:Gauss law states that electric flux through any closed surface is equal to the net charge enclosed inside the surface divided by the permittivity of vacuum.Electric field due to a uniformly charged thin shell:In the diagram, O is the centre of the spherical shell of radius R, and charge enclosed by the spherical shell is q.Let a point A is outside the spherical shell, where we have to calculate the electric field.The distance between the centre of spherical shell and the point A.ϕ=E.ScosθSo, ϕ=E.4πr2−−−−−−−−−−−−−−(1)As per gauss law,ϕ=qϵo−−−−−−−−−(2)From equation (1) and (2)E.4πr2=qϵoNow,E=q4πϵor2This is the electric field at the distance r, outside from the shell.

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