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 . see in the image there is a circular loop through which current flows and white one is amperian loop and we have to find magnetic field at point p


1 Answer 1


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.

  • $\begingroup$ 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 $\endgroup$
    – Debakant
    Commented Oct 21, 2020 at 8:52
  • $\begingroup$ @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. $\endgroup$
    – ProfRob
    Commented Oct 21, 2020 at 11:54

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