Expression of current in multilayer coils... ?

[chromatik]

Dear all,

I was asking myself if there's an expression of the B-field produced by a solenoid coil.
For a single layer, this is quite easy:
B = mu * N * I
where mu is the permeability, N is the number of turns and I the injected current.

But when you have X layers, how does this working ?

I'm working on it, but if you have some kind of advice or paper that could help me, that would be geat !

Thanks in advance !

 

[FvM]

Clearly, for a long (L >> D) coil, this expression is valid
H = N * I
Your expression is only valid, if µ is constant over the complete region (in- and outside the coil. In practice, it only applies for µr = 1.

Because the expression doesn't contain a D parameter, it would be valid also for multiple layers of different diameter. But I doubt, that it helps with practical solenoid problems. In the general case, you can integrate Biot-Savarts rule to get the field of arbitrary rotation symmetrical coil geometries. But it still doesn't describe fields of coils with inhomogenous µr, e.g. any solenoid with a core. Except for very simple cases, numerical methods are required for an exact solution.

The right forum would be Mathematics & Physics or Electronic Elementary Questions, I think.

 

[chromatik]

And more, this equation is valid for a long coil, I mean the diameter is really smaller than the length.

Thanks, I will switch to the appropriated section.
If any moderator can do the little work ... ?