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I was wondering if someone could please help explain the directional behaviour of the magnetic vector potential? I understand that the magnetic vector potential $A$ is perpendicular to $B=∇×A$ but can someone please help explain why this is true?

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The vector potential is defined by ${\bf B}=\nabla \times {\bf A}$, but it is not uniquely defined. You can add the gradient of any scalar function to ${\bf A}$ and ${\bf B}$ will be unchanged.

That being true, then the vector potential could be in any direction.

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    $\begingroup$ In particular, the OP's assertion that the vector potential is perpendicular to the magnetic field is not necessarily true. $\endgroup$ Nov 24, 2021 at 19:13

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