Ampere's Law-when does it work?

• JasonBourneV
In summary, I don't think so because path must cross through center of our interest, and here it isn't.
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?

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?

1. What is Ampere's Law?

Ampere's Law is a fundamental law in electromagnetism that describes the relationship between electric current and magnetic fields.

2. When does Ampere's Law work?

Ampere's Law works in situations where there is a steady current flowing through a closed loop or path. It also works when the magnetic field is constant in both magnitude and direction.

3. What is the formula for Ampere's Law?

The formula for Ampere's Law is ∫B·dl = μ₀I, where B represents the magnetic field, dl represents the differential length along the closed path, μ₀ is the permeability of free space, and I is the current passing through the loop.

4. What are some practical applications of Ampere's Law?

Ampere's Law is used in the design of electrical devices such as motors, generators, and transformers. It is also used in the analysis of circuits and in the study of electromagnetic radiation.

5. Is Ampere's Law always accurate?

Ampere's Law is accurate in most situations, but it may not fully describe the behavior of magnetic fields in some cases, such as when there are changing electric fields or when the magnetic field is not uniform. In these cases, the more general Maxwell's equations are needed.

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