Question

Using application of Gauss's law find the electrical field to uniformly charge thin shell in case of point lies outside, on the surface & inside the charge shell. 

Answer 1

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.