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I want to calculate the magnetic scalar and vector potentials for an infinite axial current density given as \begin{equation} J(r,\varphi) = \frac{I}{R} \delta(r-R) \sin\varphi \cos\varphi \bf{\hat{k}}. \end{equation} For the vector potential, I think I need to go with the following integral
\begin{equation} \mathbf{A} (\mathbf{x}) = \frac{\mu_0}{4 \pi} \int \frac{\mathbf{J(x')}}{\bf|x-x'|}d^3x' \end{equation} I think I need some simplifications at this point but couldn't come up with anything.

As for magnetic scalar potential, I am confused. It says (https://en.wikipedia.org/wiki/Magnetic_scalar_potential) it is only defined in regions where there is no current. Then how to calculate it?

Any help is appreciated!

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  • $\begingroup$ I think I need some simplifications. The delta function simplifies the integral over $r’$. $\endgroup$
    – Ghoster
    Jul 21, 2023 at 22:51
  • $\begingroup$ magnetic scalar potential … is only defined in regions where there is no current Which is almost everywhere. $\endgroup$
    – Ghoster
    Jul 21, 2023 at 22:54

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