ElectricDipole - Electric Dipole fields.,E, onitsaxis....

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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  equation.
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