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Ampere's law with current loop

  1. Dec 13, 2015 #1
    Is it possible to find the magnetic field on the axis above a current loop using Ampere's law? I was thinking you could treat an infinitesimal piece of the loop as a straight wire and draw a circle around it with radius sqrt(a^2 + z^2), with a=radius of current loop and z=position of point of interest, and take the integral of B around the big circle, then multiply by 2*pi*a*cos(theta) to get the full contribution in the right direction. I tried doing this but it doesn't work. Is there a reason I can't use Ampere's law for a circular current loop? In general, do we have to use Biot-Savart for this configuration, or is there some way to use Ampere?
    Last edited: Dec 13, 2015
  2. jcsd
  3. Dec 13, 2015 #2


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    Gold Member

    Yes, in general you have to use B-S to find the B-field at some specific location, because the circulation integral in Amperes law only speaks about the mean value of the H-field, following some circulation path.

    However there are exceptions. For example you can calculate the H-field in the middle of an infinit long solenoid, by choosing a "smart" circulation path:


    And of course you can also find the H-field in a toroid due to the symmetry.
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