I'm having a hard time proving that if [tex]A=k \frac{m\times r}{(r\cdot r)^{3/2}}[/tex] (the vectorpotential of a magnetic dipole with moment [tex]m[/tex]), then:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]B=\nabla\times A=k\frac{3e_r(e_r\cdot m) -m}{(r\cdot r)^{3/2}}[/tex]

without writing the whole thing in components, which becomes long, messy and ugly.

What's the elegant way of proving the magnetic induction [tex]B[/tex] in vectorial form from the vector potential [tex]A[/tex]?

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# Basic vector calculus

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