Current loop + perpendicular current : magnetic field?

In summary, the conversation is about constructing a superposition of magnetic fields for a tokamak-related diploma thesis. The first task is to find the magnetic field due to a current loop using elliptic integrals and the ellipke function in Matlab. Then, a perpendicular current is added at the center of the loop and the total magnetic field is plotted. The issue now is when the perpendicular current is not at a right angle and is no longer at the center of the loop. The solution involves transforming between cylindrical coordinates and using a 2-d rotation matrix.
  • #1
el_greco
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Homework Statement


Hi, it's my first post and I'm not sure whether it's the right category to post anyway. Please help me though :) I have to "construct" theoretically a superposition of magnetic fields for the introduction of my tokamak-related diploma thesis. First task was to find the magnetic field due to a current loop, which was done with elliptic integrals and the ellipke function in matlab. Then I had to superimpose a perpendicular current at the centre of the loop and plot the total magnetic field. That was easy, since I just had to add a new quantity to the already existing Br part of the current loop imposed field.

My problem now is what happens when the perp. current is not perp. any more, but crosses the plane of the loop at an angle theta. What's more, it's not even in the centre anymore, but at some other part of the diameter, along the r axis of the cylindrical system.

What is the specific change at the coordinates' system I have to apply so as to express the new magnetic field in the old coordinates, Br and Bz of the current loop (which is still there) ? Eventually I'll have to add this to my plot...

I'd appreciate any help, and please tell me whether you would like to see the m-files etc...

Thank u!
 
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  • #2
You need to tranform between cylindrical co-ordinates that are tilted relative to each other. Since the rotation is about a single rectangular axis, you can simply use the 2-d rotation matrix to achieve this. But this is only good for rectangular co-ordinates, so you'd have to convert from cylindrical to rectangular, then rotate the axes, then convert back to cylindrical and add to the field from the circular loop.

There's probably a cleverer way to do this, but the above should work.
 

1. How does a current loop create a magnetic field?

A current loop consists of a wire that forms a closed loop, with an electric current flowing through it. This current creates a magnetic field around the loop, with the direction of the magnetic field determined by the direction of the current flow. The magnetic field lines form concentric circles around the loop, with the strength of the field increasing as you move closer to the loop.

2. Can a current loop create a perpendicular magnetic field?

Yes, a current loop can create a perpendicular magnetic field by either changing the orientation of the loop or by adding a second loop with a different current direction. This perpendicular magnetic field is created when the magnetic field lines of the two loops intersect at a right angle.

3. What is the relationship between the strength of the magnetic field and the current in a loop?

The strength of the magnetic field created by a current loop is directly proportional to the current flowing through the loop. This means that increasing the current in the loop will result in a stronger magnetic field, while decreasing the current will result in a weaker magnetic field.

4. How does the size and shape of a current loop affect the magnetic field it creates?

The size and shape of a current loop can affect the strength and direction of the magnetic field it creates. A larger loop with more turns will generally result in a stronger magnetic field, while a smaller loop with fewer turns will result in a weaker magnetic field. The shape of the loop can also affect the direction of the magnetic field, as the field lines will follow the shape of the loop.

5. What are some practical applications of a current loop with a perpendicular magnetic field?

A current loop with a perpendicular magnetic field has many practical applications. It is commonly used in electric motors, generators, and transformers to convert electrical energy into mechanical energy and vice versa. It is also used in MRI machines to create a strong magnetic field to produce detailed images of the body. Additionally, it is used in particle accelerators to guide and manipulate charged particles.

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