Electric field due to uniformly charged thin shell—
If point lies outside the shell.
Let us consider a thin spherical shell of radius “r”. Its surface charge density “σ”. Its charge distribution is uniform. By defn of surface charge density
Eqn 4 is general eqn for electric field due to uniformly charged thin shell. If point P lies outside the shell
Case-II If point P lies on the surface of shell.
In this case radius of original shell and Gaussian sphere are equal
Eqn 5 is general expression for electric field when point is on the surface of shell.
Case-III. If point lies inside the uniformy chared shell.
According to Gauss Law
ϕ = q/ε0 ...(6)
Where q is enclosed surface charge but Gaussian surface enclose no charge.
q = 0 ....(7)
ϕ = 0/ε0 = 0 ε = 0 ....(8)
Inside the thin spherical shell electric field is zero.