Ampere's Law-when does it work?

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The discussion revolves around the application of Ampère's Law in determining the magnetic field in specific geometries, particularly a square loop and a circular loop formed by a current-carrying conductor. Participants are exploring the conditions under which Ampère's Law is applicable and questioning the uniformity of the magnetic field in these scenarios.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are debating whether Ampère's Law can be applied to find the magnetic field at the center of a square loop and a circular loop. Some suggest that it may not be applicable due to the lack of symmetry, while others propose that careful consideration might allow for its use. Questions about the uniformity of the magnetic field and the validity of specific approaches are also raised.

Discussion Status

The discussion is active, with participants offering differing viewpoints on the applicability of Ampère's Law. Some guidance has been provided regarding the conditions under which the law is typically effective, and there is an ongoing exploration of the implications of symmetry in these cases. There is no clear consensus yet, as participants continue to question and clarify their understanding.

Contextual Notes

Participants are operating under the assumption that the magnetic field's uniformity is a critical factor in applying Ampère's Law. There is also a recognition that the complexity of the geometry may influence the ease of applying the law.

JasonBourneV
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Can Ampère’s law be used to find the magnetic field at the center of a square loop carrying a constant current?
How about at the center of a circle formed by a current-carrying conductor.


In both cases, I don't think so because path must cross through center of our interest, and here it isn't. Am I correct?
 
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Ampere's law really only works for long symmetric things. The three most common examples are a sheet of current, an infinite solenoid (a bunch of circular wires stacked up), and a toroid (wires wrapped around a doughnut). For the square loop you have to use Biot-Savart as well as the center of a current-carrying conductor, especially because the surface current could travel in all kind of directions.
 
wait, can't we still use ampere's law for a square loop as long as we are careful about it. I think the magnetic field in the loop in uniform, is it not? If it is then can't we make an amperian loop just bigger than the square so the radius of the circle equals L/sqrt(2) then u get B = [(mu)isqrt(2)]/[2(pi)L] which is the same I get when using biot-savart. Is my reasoning correct? or is this just a fluke that the answer's the same?
 
Fusilli_Jerry89 said:
wait, can't we still use ampere's law for a square loop as long as we are careful about it. I think the magnetic field in the loop in uniform, is it not? If it is then can't we make an amperian loop just bigger than the square so the radius of the circle equals L/sqrt(2) then u get B = [(mu)isqrt(2)]/[2(pi)L] which is the same I get when using biot-savart. Is my reasoning correct? or is this just a fluke that the answer's the same?

Ampere's law is always valid. The real question is whether it is easy to work with or not. Unless you have a lot of symmetry in the system, the integral will be impossible to carry out so it won't be a useful approach.

And no, the B field is not uniform in your example.
 
oh woops yeah stupid me it's not uniform. But is my approach valid for the point in the centre of the square loop? Is this where the magnetic field is largest?
 

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