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Surface Charge Density of a Charged Conductor

The excess charge resides on the surface of the conductor. But its distribution over the surface may not be uniform. The charge density s is maximum where the radius of curvature is minimum and vice versa. That is

s µ

Proof: As a conductor is an equipotential VS = constt. In case of spherical conductor,

with q = 4pR2 s

So = constt., Þ sR = constt. Þ s µ (1/R)

This is the reason why lightning rods are made sharply pointed at the top. These rods help protecting tall buildings from lightning by conducting the charge of the cloud to the ground.

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