The field due to multiple concentric solenoids with water

[Jeremy_W]

Homework Statement

OK, so I am doing research this semester and I am working with the Faraday effect. For my magnetic field, we are using a large solenoid that is comprised of 13 concentric solenoids each of which has the same number of coils per unit length. In between each of these layers there are layers of water to cool the wires to prevent overheating and of course in the middle is the substance which the light will pass through. However, for this calculation, I will assume it to be a vacuum (under the instruction of the professor). So I need to calculate the magnetic field strength.

Homework Equations

Ampere's Law: ∫B.ds=μ_OJ
Magnetic Field of one solenoid with a non-vacuum core: B = μnI

The Attempt at a Solution

Well, I read in another thread that the magnetic field in the center is simply the magnetic field due to the inner most one. And when I use Ampere's Law, I get the same thing. So basically, I am getting:

B = μ n_inner I

 

[hikaru1221]

If B is just due to the most inner one, then throw away the other solenoids
Imagine that all the solenoids have nearly the same radius, then if you stand in the center, what you see is one solenoid with current 13I, not I.