# Using application of Gauss's law find the electrical field to uniformly charge thin shell in case of point lies outside,

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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.

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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.