# Electromagnetism Public

## Foundations of Electromagnetism and Optics

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## Module Information

### Vector Calculus Revision

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

Charge Density Point Charge and the δ-distribution Coulomb's Law Electric Field
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### 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&gt;&gt;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-&gt;0,q-&gt;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 ...
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