produced by Motion in the Electric Field.
7
Equating the coefficients of to zero in equations (2) and (3) we have
inside the sphere,
with similar equations for and ; outside the sphere we have
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(4)
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with similar equations for and .
The form of equation (4) suggests that we should put
A particular integral of (4) is then
The complementary function is that solution of the differential equation
which, when considered as a function of the angular coordinates of a point, varies as ; this (see Proc. Math. Soc. vol. xv. p. 212) is
where
and
Thus, outside the sphere,
where , and is introduced into the expression