Electric Dipoles and Multipoles

Lecture 5

Def. Dipole - An e dipole is formed by 2 +/- point charges, +q/-q

ElDipole moment, Cm

See Figure 8 in notes

Field of an electric dipole

Potential from superpositon - see Eqn 53

Considering the far field limit [r>>a], use Taylor expansion to get Eqn 54, the far-field limit of potential, which is a solution of the Laplace eqn [div^2]

For electric field, use the gradient identity as seen in Eqn 55. It's components are simplest in spherical coords (see Eqn 56)

Ideal Dipole - limit a->0,q->infinity with  p=constant

Physical dipole - fill solution see eqn 57

The sketches (F9) for these electric fields are slightly different

Dipole Interaction with the External Electric FIeld

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Multipole Expansions

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