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I Confusion regarding line integrals

  1. May 3, 2017 #1
    Sorry if this is the wrong place to post this, but I wasn't sure where exactly to put it.
    When we calculate the force on a closed loop of current-carrying wire in a uniform magnetic field,
    We calculate the line integral of the loop to be 0.
    However, when we evaluate the line integral for an Amperian loop while using Ampere's law, we integrate from 0 to 2π.
    Why is there a difference? I'm not very advanced with calculus, so some intuition is all I request.
  2. jcsd
  3. May 3, 2017 #2


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    I am not sure I understand what you are asking. Both line integrals are taken over closed loops, so if your variable of integration is some angle θ, then the limits of integration would be from 0 to 2π. The fact that the net force on a current loop in a uniform magnetic filed is zero is a different issue. Think of the integral as a sum. In the current loop case you are adding a whole bunch of elements ##d \vec{F}## that point in all sorts of directions so that their sum is zero regardless of the shape of the loop. In the Amperian loop case, you choose the loop so that the B-field is tangent to the loop in which case all the ##\vec{B}\cdot d\vec{\mathcal l}## terms add together to give a non-zero value.

    I hope I answered your question.
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