Coulomb-gauge vector potential of a localized steady current

\nabla \cdot J = 0

and the current decays enough for boundary terms to vanish, then

A (x) = \frac{μ _{0}}{4 π} \int \frac{J ( x ^{'} )}{∣ x - x ^{'} ∣} d^{3} x^{'}

satisfies

\nabla \cdot A = 0

. Its far field is

A (x) = \frac{μ _{0}}{4 π} \frac{m \times x}{∣ x ∣ ^{3}} + \dots .

 Ancestors (6)