Electromagnet with multiple layers of wire

Question

It is well known that the magnetic field inside an electromagnet can be given by $B=k\mu_0nI$, where $k$ is a constant related to the material inside, $\mu_0$ is a constant, $n$ is the number of turns per unit length, and $I$ is the current.

However, all explanations of this concept seem to assume that the number of turns is limited by the width of the wire because every loop of the wire must touch the internal conductor. What if, in order to increase the number of turns per unit length above what the width of the wire would otherwise allow, one were to make multiple loops of wire on top of one another so that the outer loops did not touch the iron (or whatever) material inside the electromagnet? Would it still increase the strength of the magnetic field? Proportionally to the number of turns per unit length, or less than proportionally to the number of turns per unit length?

Thank you.

Answer 1

Each turn of the wire centered at the same position contributes roughly the same (there is slight difference due to the fact that additional turns at the same position will have slightly larger radius). For two-layer solenoid, the formula would be similar to one-layer solenoid, there would just be a factor of two.