Find the electric field intensity due to a uniformly charged spherical shell at a point (i) outside the shell and (ii) inside the shell. Plot the graph of electric field with distance from the centre of the shell.

Consider a thin spherical shell of radius R with a positive charge q distributed uniformly on the surface. As the charge is uniformly distributed, the electric field is symmetrical and directed radially outward
(i) Electric field outside the shell:
For pointr>R; draw a spherical gaussian surface of radius r.Using gauss law,∮E.ds=q/ε₀
Since →E is perpendicular to gaussian surface, angle between →E is 0.Also →E being constant, can be taken out of integral.So,E(4πr²)=q/ε₀
So,E=1/(4πε₀)q/r²
Thus electric field outside a uniformly charged spherical shell is same as if all the charge q were concentrated as a point charge at the center of the shell
(ii) Inside the shell:
In this case, we select a gaussian surface concentric with the shell of radius r(r<R).
So,∮E.ds=E(4πr²)
According to gauss law,E(4πr²)=Q/ε₀
Since charge enclosed inside the spherical shell is zero.
So,E=0
Hence, the electric field due to a uniformly charged spherical shell is zero at all points inside the shell.