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Unformatted text preview: Electric Dipole Many molecules can be treated as electric dipoles for the purpose of calculating their electric fields. We can calculate the electric field, E , at a distance r from the center of the dipole at a point on its axis. The dipole has charge separation d and charges + q and –q . Using the principle of superposition, we find the following electric field along the axis connecting the two charges: E = kq/(r – d/2) 2 – kq/(r + d/2) 2 E = kq[(r – d/2)2 – (r + d/2)2 ] E = kq/r 2 [(1 – d/(2r))2 – (1 + d/(2r))2 ] If we assume that r >> d, then we can use the first two terms of the binomial expansion as follows: (1 – d/(2r))2 = 1 + d/r (1 + d/(2r))2 = 1 – d/r Substitution of the approximations into the formula for the electric fields yields the following: E = kq/r 2 [(1 + d/r) – (1 – d/r)] E = kq/r 2 [2d/r] E = 2kqd/r 3 We can use the definition of the electric dipole moment, p = qd, to further simplify the above...
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This note was uploaded on 03/10/2011 for the course PHY 112 taught by Professor Jenson during the Spring '11 term at Chemeketa.
 Spring '11
 Jenson
 Physics, Charge, Electric Fields

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