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Introduction to Electrodynamics
· Problem 3.46
Potentials — David J. Griffiths
Physics · multipole-expansion
Problem
A thin insulating rod, running from
z
=
−
a
z = -a
z
=
−
a
to
z
=
+
a
z = +a
z
=
+
a
, carries the indicated line charges. In each case, find the leading term in the multipole expansion of the potential: (a)
λ
=
k
cos
(
π
z
/
2
a
)
\lambda = k\cos(\pi z/2a)
λ
=
k
cos
(
π
z
/2
a
)
, (b)
λ
=
k
sin
(
π
z
/
a
)
\lambda = k\sin(\pi z/a)
λ
=
k
sin
(
π
z
/
a
)
, (c)
λ
=
k
cos
(
π
z
/
a
)
\lambda = k\cos(\pi z/a)
λ
=
k
cos
(
π
z
/
a
)
, where
k
k
k
is a constant.
Related theory
multipole-expansion
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