The mathematical theory of electricity and magnetism (1911)
Jeans, James Hopwood, Sir, 1877-1946 · Cambridge [Eng.] : University Press · leaf 234
find the potential of a spherical capof angle a—i.e. the surface cut from a sphere bya right circular cone of semivertical angle a—electrified to a uniform surface density o-o. We can regard this as a complete sphereelectrified to surface density cr, where (T = (Tff from ^ — 0 to 6 — a,a=0 from 6 =… … Fig. 76. e=i aPn (cos 6) d (cos 6) In +1 r^=^ —^— o-o Pn (cos 6) d (cos 6) ^ J 9 = a = I o-o [Pn-x (cos a) - i?i+i (cos a) by equation (165), except when n =0. For this case we have C^o ~ 2 ^0 9 = 0 e=a d (cos ^) = ^ o-o (1 — cos a). Thus o- = io-o (1 - cos a) + X \Pn-\ (cos a) — i?j+i (cos a)\ P^…
Electricity · Magnetism
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