P23_017 - qd/ 2 πε ( z − d/ 2) 3 and the Feld produced...

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17. Think of the quadrupole as composed of two dipoles, each with dipole moment of magnitude p = qd . The moments point in opposite directions and produce Felds in opposite directions at points on the quadrupole axis. Consider the point P on the axis, a distance z to the right of the quadrupole center and take a rightward pointing Feld to be positive. Then, the Feld produced by the right dipole of the pair is
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Unformatted text preview: qd/ 2 πε ( z − d/ 2) 3 and the Feld produced by the left dipole is − qd/ 2 πε ( z + d/ 2) 3 . Use the binomial expansions ( z − d/ 2) − 3 ≈ z − 3 − 3 z − 4 ( − d/ 2) and ( z + d/ 2) − 3 ≈ z − 3 − 3 z − 4 ( d/ 2) to obtain E = qd 2 πε · 1 z 3 + 3 d 2 z 4 − 1 z 3 + 3 d 2 z 4 ¸ = 6 qd 2 4 πε z 4 . Let Q = 2 qd 2 . Then, E = 3 Q 4 πε z 4 ....
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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