#jackson electrodynamics

Dipole field from multipole moment sum

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As indicated in Jackson [1], the components of the electric field can be obtained directly from the multipole moments

\begin{equation}\label{eqn:dipoleFromSphericalMoments:20} \Phi(\Bx) = \inv{4 \pi \epsilon_0} \sum \frac{4 \pi}{ (2 l + 1) r^{l + 1} } q_{l m} Y_{l m}, \end{equation}

so for the \( l,m \) contribution to this sum the…

Magnetostatic force and torque

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In Jackson [1], the following equations for the vector potential, magnetostatic force and torque are derived

\begin{equation}\label{eqn:magnetostaticsJacksonNotesForceAndTorque:20} \Bm = \inv{2} \int \Bx’ \cross \BJ(\Bx’) d^3 x’ \end{equation} \begin{equation}\label{eqn:magnetostaticsJacksonNotesForceAndTorque:40} \BF = \spacegrad( \Bm…

Magnetic moment for a localized magnetostatic current

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Motivation.

I was once again reading my Jackson [2]. This time I found that his presentation of magnetic moment didn’t really make sense to me. Here’s my own pass through it, filling in a number of details. As I did last time, I’ll also translate into SI units as I go.

Vector potential.

The Biot-Savart expression for the magnetic field…