<Dl> <Dd> E (R) = 3 (p ⋅ R ^) R ^ − p 4 π ε 0 R 3 . (\ displaystyle \ mathbf (E) \ left (\ mathbf (R) \ right) = (\ frac (3 \ left (\ mathbf (p) \ cdot (\ hat (\ mathbf (R))) \ right) (\ hat (\ mathbf (R))) - \ mathbf (p)) (4 \ pi \ varepsilon _ (0) R ^ (3))) \ .) </Dd> </Dl> <Dd> E (R) = 3 (p ⋅ R ^) R ^ − p 4 π ε 0 R 3 . (\ displaystyle \ mathbf (E) \ left (\ mathbf (R) \ right) = (\ frac (3 \ left (\ mathbf (p) \ cdot (\ hat (\ mathbf (R))) \ right) (\ hat (\ mathbf (R))) - \ mathbf (p)) (4 \ pi \ varepsilon _ (0) R ^ (3))) \ .) </Dd> <P> Thus, although two closely spaced opposite charges are not quite an ideal electric dipole (because their potential at short distances is not that of a dipole), at distances much larger than their separation, their dipole moment p appears directly in their potential and field . </P> <P> As the two charges are brought closer together (d is made smaller), the dipole term in the multipole expansion based on the ratio d / R becomes the only significant term at ever closer distances R, and in the limit of infinitesimal separation the dipole term in this expansion is all that matters . As d is made infinitesimal, however, the dipole charge must be made to increase to hold p constant . This limiting process results in a "point dipole". </P>

When is the net torque on an electric dipole in an electric is field maximum