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Using Gauss’s law obtain the expression for the electric field due to a uniformly charged thin spherical shell of radius R at a point outside the shell. Draw a graph showing the variation of electric field with r, for r > R and r < R.

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Consider a thin spherical shell of radius R carrying charge Q. To find the electric field outside the shell, we consider a spherical Gaussian surface of radius r (> R), concentric with given shell. The electric field vector E is same at every point of Gaussian surface and directed radially outwards (as is unit vector n so that q = 0°)

According to Gauss’s theorem,

Hence, electric field outside a charged thin spherical shell is the same as if the whole charge Q is concentrated at the centre.

The variation of electric field vector E with distance from centre of a uniformly charged spherical shell is shown in figure.

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