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 .
1 Answer
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You could, but unclear how this helps you. Ampere's law would, in this case, tell you that $$ \oint \vec{B}\cdot d\vec{l} = 0\ ,$$ 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.
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$\begingroup$ You mean through, not inside the loop .i.e current should pass the cross section of a linear closed loop not reside on the same plane $\endgroup$– DebakantCommented Oct 21, 2020 at 8:52
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$\begingroup$ @Debakant The RHS is $\int \vec{J} \cdot d\vec{A}$, where the surface integral is taken over a (any) surface bounded by the closed loop. This must be zero for the loop and current shown. $\endgroup$– ProfRobCommented Oct 21, 2020 at 11:54