Ampere's Law-when does it work?

[JasonBourneV]

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?

 

[Mindscrape]

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.

 

[Fusilli_Jerry89]

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?

 

[nrqed]

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.

 

[Fusilli_Jerry89]

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?