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Unformatted text preview: ~ R V = 1 4 X l =0 i q i r l i P l (cos i ) R l +1 Or if we have a continuous distribution ( ~ r ), V = 1 4 X l =0 R R R r l P l (cos ) d R l +1 Lowest order term l = 0, is just the total charge, V 1 R Q = Z Z Z d Multipole expansion, continued Next order term l = 1 is the dipole moment, V 1 R 2 p = Z Z Z r cos d Writing both the l = 0 (monopole) and l = 1 (dipole) terms, we have V = 1 4 Q R + p R 2 + ... Higher order terms take into account more details of the distribution with contributions that fall o faster with increasing R For example, the quadrupole moments contribute a potential 1 R 3...
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 Spring '03
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