Ampere's law with current loop

In summary, it is generally necessary to use Biot-Savart to find the magnetic field at a specific location, as Ampere's law only accounts for the mean value of the H-field along a circulation path. However, there are exceptions such as calculating the H-field in the middle of an infinitely long solenoid by choosing a specific circulation path. The same applies for finding the H-field in a toroid due to symmetry.
  • #1
Sturk200
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Is it possible to find the magnetic field on the axis above a current loop using Ampere's law? I was thinking you could treat an infinitesimal piece of the loop as a straight wire and draw a circle around it with radius sqrt(a^2 + z^2), with a=radius of current loop and z=position of point of interest, and take the integral of B around the big circle, then multiply by 2*pi*a*cos(theta) to get the full contribution in the right direction. I tried doing this but it doesn't work. Is there a reason I can't use Ampere's law for a circular current loop? In general, do we have to use Biot-Savart for this configuration, or is there some way to use Ampere?
 
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  • #2
Sturk200 said:
In general, do we have to use Biot-Savart for this configuration, or is there some way to use Ampere?
Yes, in general you have to use B-S to find the B-field at some specific location, because the circulation integral in Amperes law only speaks about the mean value of the H-field, following some circulation path.

However there are exceptions. For example you can calculate the H-field in the middle of an infinit long solenoid, by choosing a "smart" circulation path:

http://physics.stackexchange.com/questions/112155/using-amperes-law-for-a-solenoid

And of course you can also find the H-field in a toroid due to the symmetry.
 

1. What is Ampere's law with current loop?

Ampere's law with current loop is a fundamental law in electromagnetism that describes the magnetic field generated by a closed loop of electric current. It states that the magnetic field at any point around the loop is directly proportional to the current passing through the loop and inversely proportional to the distance from the loop.

2. How is Ampere's law with current loop derived?

Ampere's law with current loop is derived from the Maxwell-Ampere equation, which is a modified version of Ampere's law that includes a term for the displacement current. This term takes into account the changing electric field that is created by a time-varying magnetic field.

3. What is the significance of Ampere's law with current loop?

Ampere's law with current loop is significant because it allows us to calculate the magnetic field produced by a closed loop of current. This is important in understanding and designing devices that use electromagnets, such as motors, generators, and transformers.

4. Can Ampere's law with current loop be used to calculate the magnetic field at any point in space?

No, Ampere's law with current loop is only applicable to situations where the current is constant and the magnetic field is symmetric around the current-carrying loop. For more complex situations, such as varying currents or non-uniform magnetic fields, other equations and techniques must be used.

5. How does the direction of the magnetic field change with respect to the current in Ampere's law with current loop?

The direction of the magnetic field follows the right-hand rule. If you point your right thumb in the direction of the current flow, the curl of your fingers will point in the direction of the magnetic field. This rule applies at every point around the loop, allowing us to determine the direction of the magnetic field at any point using Ampere's law with current loop.

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