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Magnetic dipole moment

{c}

If $\nabla\cdot J=0$ and the current decays enough for boundary terms to vanish, then
$$
A(x)=\frac{\mu_0}{4\pi}\int\frac{J(x')}{|x-x'|}\,d^3x'
$$
satisfies $\nabla\cdot A=0$. Its far field is
$$
A(x)=\frac{\mu_0}{4\pi}\frac{m\times x}{|x|^3}+\cdots.
$$


Coulomb-gauge vector potential of a localized steady current

Past exam of the mathematics course of the University of Cambridge / 2016 / ia / Paper 3 / 11C / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 1 / 15C / Solution

Coulomb-gauge vector potential of a localized steady current

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Coulomb-gauge vector potential of a localized steady current

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