Ampere's law: the position of amperian loop

Question

Can Amperian loop be taken parallel to current. I.e suppose current is in a circular loop in xy plane. And let the screen you are watching is xy plane . Can we take amperian loop in the same plane.
And find out magnetic field at a point .

ProfRob · Answer

You could, but unclear how this helps you. Ampere's law would, in this case, tell you that
$$ oint vec{B}cdot dvec{l} = 0 ,$$
because you have no current flowing through the closed loop.
I suppose it does tell you there isn't a toroidal field aligned with the Amperian loop.

Ampere's law: the position of amperian loop

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