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# A Thin Conducting Spherical Shell of Radius R Has Charge Q Spread Uniformly Over Its Surface. Using Gauss’S Law, Derive an Expression for an Electric Field at a Point Outside the Shell. - Physics

#### Question

A thin conducting spherical shell of radius R has charge Q spread uniformly over its surface. Using Gauss’s law, derive an expression for an electric field at a point outside the shell.

#### Solution

According to Gauss law,

epsi_0EointdA=q

Where,

q is the point charge

E is electric field due to the point charge

dA is a small area on the Gaussian surface at any distance and

epsi_0 is the proportionality constant

For a spherical shell at distance r from the point charge, the integral ointdA is merely the sum of all differential of dA on the sphere.

Therefore, oint dA =4pir^2

epsi_0E(4pir^2) = q

or ,E = q/(epsi4pir^2)

Therefore, for a thin conducting spherical shell of radius R and charge Q, spread uniformly over its surface, the electric field at any point outside the shell is

E = Q/(e_0 4pir^2)

Where r is the distance of the point from the centre of the shell.

E = q/(4piepsi_0r^2)

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