An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism

George Green

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1828 Excerpt: ...on the surface in question. Suppose now, all the interior bodies to reduce themselves to a single point P, in which a unit of electricity is concentrated, and f to be the distance Pp': the potential function arising from P will be-L, and hence B'=L. f r' being, as before, the distance between p' and the centre O of the shell. Let now b represent the distance OP, and e the angle POp', then will f=b3--2br'. cos o+r'. From which equation we deduce successively, df _ 6cog 8 dB' _ 2 / if _--2S+ 26.cos.fl Making r'=a in this, and in the value of B' before given, in order to obtain those which belong to the surface, there results This substituted in the general equation written above, there arises 6«--«» i--r 4raft If P is supposed to approach infinitely near to the surface, so that J=a--; « being an infinitely small quantity, this would become In the same way, by the aid of the equation between A and p, the density of the electric fluid, induced on the surface of a sphere whose radius is a, when the electrified point P is exterior to it, is found to be _ ««--5« P ATraf, supposing the sphere to communicate, by means of an infinitely fine wire, with the earth, at so great a distance, that we might neglect the influence of the electricity induced upon it by the action of P. If the distance of P from the surface, be equal to an infinitely small quantity, we shall have in this case, as in the foregoing, From what has preceded, we may readily deduce the general value of V, belonging to any point P, within the sphere, when V its value at the surface is known. For fpj, the density induced upon an element da of the surface, by a unit of electricity concentrated in P, has just been shown to be 4«--«« f being the distance P,...

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ISBN 10:  1173567852 ISBN 13:  9781173567859
Publisher: Nabu Press, 2011
Softcover