# Off-axis Magnetic Field of Current loop (MATLAB?)

• MATLAB
• dave_western
In summary, you can use Matlab to calculate the fields due to a current loop off-axis. However, this will require a numerical approximation. If you are confused, you can type "help ellipke" in the Matlab command line for more help.
dave_western
I have checked the forums for similar problems and have only seen that one would use 'MATLAB' to perform this integration.

All I want to do is find the 3 components of the magnetic field at a point (x, y, z) off of the axis of a current loop (given current, radius and that the loop lies on the xy plane centered at the origin).

Can someone point me in the right direction to even get started on this problem? I have been told that this is achievable in Excel!

Any help would be awesome!

If I'm not mistaken, this would involve a so-called "elliptic integral".
You may have to resort to numerical approximations.

I was hoping that would be the case, but I haven't had any luck finding a numerical approximation for a circle.

Diameter=1m
Centered on origin
Lying on x-y plane

Can anyone help?

I don't think you're understanding this correctly. When robphy said that you have to do numerical approximations, what he meant was that the solution to that problem cannot be solved analytically. Furthermore, you won't have a simple, closed form solution. What you will have is an infinite series.

So you have to solve the differential equation numerically and obtain an approximate answer based on where you truncate the series. It doesn't mean that you find a "numerical approximation for a circle".

Please refer to Jackson's classic text on this where this example is illustrated using Green's function technique.

Zz.

i use simple code written in fortran for calculating magnetic fields in the space due to any shaped current carrying loop,,,,,just give the input file with geometry of the loop as a summation of straight and arcs and ask the magnetic field in the space in RZT or XYZ system,,,that's it...i use to calculate the fields due to PF and TF coil system in a tokamak

This was posted years ago, but incase someone else is searching through this (as I was), you can use Matlab quite easily to calculate this.

You can use the equations found here:

http://www.netdenizen.com/emagnet/offaxis/iloopoffaxis.htm

They are simple equations which you just plug in the values for the variables. The only confusing thing is the complete elliptic integrals which Matlab can also calculate for you.

Use the Matlab function [K,E] = ellipke(k^2) to calculate the complete elliptic integrals of the first and second kind, E(k) and K(k).

Remember to give k^2 as the argument in Matlab function. If you're confused type "help ellipke" in the Matlab command line.

## What is the Off-axis Magnetic Field of a Current Loop?

The off-axis magnetic field of a current loop refers to the magnetic field that is produced by a circular loop of electric current in a direction perpendicular to the axis of the loop. This field is strongest at the center of the loop and decreases as the distance from the center increases.

## How is the Off-axis Magnetic Field of a Current Loop Calculated?

The off-axis magnetic field of a current loop can be calculated using the Biot-Savart Law, which states that the magnetic field at a point due to a current-carrying wire is directly proportional to the current, the length of the wire, and the sine of the angle between the wire and the line connecting the point to the wire.

## What is the Relationship Between the Off-axis Magnetic Field and the Current in a Loop?

The off-axis magnetic field of a current loop is directly proportional to the amount of current flowing through the loop. This means that as the current increases, the strength of the magnetic field also increases.

## How Does the Shape and Size of a Loop Affect the Off-axis Magnetic Field?

The shape and size of a loop can significantly affect the strength of the off-axis magnetic field. A larger loop will produce a stronger magnetic field, while a smaller loop will produce a weaker field. The shape of the loop can also impact the distribution of the magnetic field, with non-circular loops producing more complex field patterns.

## Can MATLAB be Used to Calculate the Off-axis Magnetic Field of a Current Loop?

Yes, MATLAB can be used to calculate the off-axis magnetic field of a current loop. The Biot-Savart Law can be implemented in MATLAB to calculate the field at specific points, and the resulting data can be visualized using various plotting functions.

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