Reprint of papers on electrostatics and magnetism . rc from G to thelip; and (15) becomes _ 1 q /CQ^ — a^ ryjx ^~2iT^ aP^^ a^-GP^ ^ which is the result stated in § 219, above. It is remarkablethat this expression is independent of the radius of the spheri-cal surface of which the bowl is a part. Hence, if we supposethe radius infinite, we have the same expression (17) for theelectric density at any point P on either side of an infinitelythin circular disc of radius a, connected with the earth by aninfinitely fine wire, and influenced by a quantity Q of electricitycollected at any point Q in th
Reprint of papers on electrostatics and magnetism . rc from G to thelip; and (15) becomes _ 1 q /CQ^ — a^ ryjx ^~2iT^ aP^^ a^-GP^ ^ which is the result stated in § 219, above. It is remarkablethat this expression is independent of the radius of the spheri-cal surface of which the bowl is a part. Hence, if we supposethe radius infinite, we have the same expression (17) for theelectric density at any point P on either side of an infinitelythin circular disc of radius a, connected with the earth by aninfinitely fine wire, and influenced by a quantity Q of electricitycollected at any point Q in the plane of the disc, but outsideits bounding circle. It agrees with the solution previouslygiven by Green for this case in his paper referred to in § 234,above. 240. (Compare § 220.) To find the distribution for the casein which S is insulated, electrified, and removed from all dis-turbing influence, let F be the constant potential producedthroughout S by this distribution. Eemark that the same 184 Distribution of Electricity on Circular [ distribution of electricity on S would be produced inductively if it were connected by an infinitelyfine wire with the earth, and en-closed by any surface, EE, rigidlyelectrified with such a quantity anddistribution of electricity as (§§ 5,73, 206, 207; also Thomson andTait, § 499) to produce a uniformpotential — V through its take this enclosing surface,EE, to be spherical, concentric with that of which 5 is a part,and of radius greater than that of the last mentioned by aninfinitely small excess. The electric density of the inducing Vdistribution will be uniform all over EE, and equal to — —-. 2irf if / be the diameter of the surface. The portion of EE which lies infinitely near to the convex surface of 8 will clearly induce on this convex surface an equal electric density of contrary Vsign, that is, 4-t—>.• The remainder of EE will induce equal 27!/ electric densities on the concave and convex sides of
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectmagnetism, bookyear18
