Using Gauss's Theorem, Derive an expression for electric field intensity due to uniformity charged hollow sphere : (b) At a point on the shell

Explanation

Electric field intensity at a point on the surface of shell.
Let P be the point on the surface of spherical shell such that `r=R`
According to Gauss theorem
`:." "underset(S)ointvecE.vec(dS)=q/varepsilon_(0)`
Since `vecE` and `vecdS` are in same direction
`:." "theta=0^(@)`
`underset(S)ointEdScos0^(@)=q/varepsilon_(0)`
`underset(S)ointEdS=q/varepsilon_(0)" "[:. "E constant"]`
`Eunderset(S)ointEdS=q/varepsilon_(0)`
`E xx 4 pi R^(2)=q/varepsilon_(0)`
`:." "E=(sigma xx cancel(4 pi R^(2)))/(cancel(4 pi R^(2)) xx varepsilon_(0))=sigma/varepsilon_(0)" "[:.q=sigma xx 4 pi R^(2)]`
`E=sigma/varepsilon_(0)`