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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.
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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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