i love electromagnetism Gradient Divergence and Gauss' Theorem Curl and Stokes' Theorem Laplacian Useful Identities 3D Taylor Expansion Important Theorem

Charge Density Point Charge and the δ-distribution Coulomb's Law Electric Field

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 ... Multipole Expansions ...