Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/251

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If, in the inverted system, the potential of the surface is unity, then the density at the point is

If, in the original system, the density at is , then

and the potential is . By placing at a negative charge of electricity equal to unity, the potential will become zero over the surface, and the density at will be

This gives the distribution of electricity on one of the spherical surfaces due to a charge placed at . The distribution on the other spherical surface may be found by exchanging and , and , and putting or instead of .

To find the total charge induced on the conductor by the electrified point at , let us examine the inverted system.

In the inverted system we have a charge at , and at , and a negative charge at a point in the line such that

If we find

Inverting this system the charges become

and

Hence the whole charge on the conductor due to a unit of negative electricity at is