Are Multiple Current Loops Linear?

[wofsy]

I assume that if one has several current loops that the magnetic fields that they generate just add together linearlly. Just want to make sure.

 

[Gear300]

Yup...that is how it looks to be (at least classically).

 

[Matterwave]

to first order they do, but I think the interaction between the current loops and other magnetic fields would induce emfs which would change the magnetic fields produced, and would further induce emfs, etc.

I suppose, if you assumed no coupling, the fields would just add linearly.

 

[wofsy]

to first order they do, but I think the interaction between the current loops and other magnetic fields would induce emfs which would change the magnetic fields produced, and would further induce emfs, etc.

I suppose, if you assumed no coupling, the fields would just add linearly.

Interesting. How would you solve this problem with coupling? The law of Biot and Savart would not work. I guess you would hold the currents in the loops constant.

 

[Matterwave]

For example, for 2 loops:

$$emf_1=\epsilon_1-\frac{d\Phi_{21}}{dt}$$

$$emf_2=\epsilon_2-\frac{d\Phi_{12}}{dt}$$

Where $$\Phi_{12}$$ that's the flux on 2 due to 1 and vice versa. It's a coupled differential equation. If you had 3 loops, you'd just have more terms and more equations. Don't quote me on this, it's been a while since I've done this stuff :P.