Calculating Force of Parallel Wires: 1 Wire & 1 Loop

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To calculate the force between a parallel wire and a loop, the equation B = μ0 I / (2 * π r) applies only under specific conditions. This equation is derived from the assumption of an infinitely long wire, which provides a symmetrical magnetic field. When dealing with a loop, this symmetry is lost, making the equation inapplicable for calculating the magnetic field produced by the loop. Therefore, while it can be used for the straight wire, alternative methods are needed to assess the magnetic field from the loop. Understanding these limitations is crucial for accurate calculations in electromagnetism.
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Homework Statement



So let's say that we have 2 wires that are parallel. To find the force that one exerts on the other I can use the equation B = μ0 I / (2 * π r), where μ0 is equal to 4(pi)e-7. But what can I do when I have 1 wire parallel to a wire that forms a loop. Will the equation still work?

Homework Equations



B = μ0 I / (2 * π r)

The Attempt at a Solution

 
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Depends. The derivation of the equation relies on a symmetry that arises because you assume the wire is infinitely long. The equation is only applicable to situations where that assumption is a good approximation, so if you want to use it to calculate the magnetic field of the wire, that's fine. You can't use it, however, to find the magnetic field due to the loop.
 

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