Using Gauss's law obtain the expression for the electric field due to a uniformly charged thin spherical shell of radius R at a point outside the shell. Draw a graph showing the variation of electric field with r, for r>R and r<R.

(i) At a point P outside the spherical shell :Let →E be the electric field at P. The electric field through an elemental surface d→s is dϕ=→E.d→s ∴Total electric flux through the gaussian surface is ϕ=∮SEds=E∮Sds=E×4πr2 ϕ=qϵ0 E×4πr2=qϵ0 E=14πϵ0.qr2 (for r>R) (ii) At a point P inside the spherical shell:In this case charge enclosed =0 E×4πr2=0 E=0 (for r<R)