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Determine the capacitance of a system consisting of a metal ball of radius a and an infinite conducting plane

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Determine the capacitance of a system consisting of a metal ball of radius a and an infinite conducting plane separated from the centre of the ball by the distance l if l >> a.

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As in 3.109 we apply the method of image. Then the potential difference between the +vely charged sphere and the conducting plane is one half the nominal potential difference between the sphere and its image and is

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