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If a charged sphere has a surface charge density of o= k cos 0 glued over its surface (where k is a constant and is the usual polar angle), then the exact potential outside the sphere is kR³ 1 360 r2 which can be derived using the method of separation of variables. V(r, 0) = cos r>R,

If a charged sphere has a surface charge density of o= k cos 0 glued over its surface (where k is a constant and is the usual polar angle), then the exact potential outside the sphere is kR³ 1 360 r2 which can be derived using the method of separation of variables. V(r, 0) = cos r>R,

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Find the approximate electrostatic potential, at points far from the sphere, and compare it to
the exact answer given above. What can you conclude about the higher multipoles?

If a charged sphere has a surface charge density of o = k cos 0 glued over its surface (where k is a constant and is the usual polar angle), then the exact potential outside the sphere is V(r, 0) kR³ 1 3€0 r2 which can be derived using the method of separation of variables. Cos 0 r≥ R,
Transcribed Image Text:If a charged sphere has a surface charge density of o = k cos 0 glued over its surface (where k is a constant and is the usual polar angle), then the exact potential outside the sphere is V(r, 0) kR³ 1 3€0 r2 which can be derived using the method of separation of variables. Cos 0 r≥ R,
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