# How does the magnetic field generated by a solenoid change depending on the type of wire?

At school to calculate the intensity of the magnetic field generated by a solenoid we use the formula:

$$B=μ_0× \frac{N}{l}×i$$

(I tried to write the formula using preformatted text, but I didn't have success even though I followed the tutorial, so I wrote it like that)

Where ;

$$μ_0 =$$ Vacuum permeability

$$N=$$ number of windings

$$l=$$ lenght of the solenoid

$$i=$$ current flowing through it

(I know that I should use the magnetic permeability of the air, but it doesn't change a lot)

I would like to know if the type of wire we use to build the solenoid can influence the magnetic field. For example, let's assume we are using a multi-strand wire. Does a solenoid made of this kind of wire behave like many parallel solenoids or it acts like a single one? And if the formula changes in some way, please explain me how. Thanks in advance.

• The equation does use $\mu_0$ which IS the permitivity of vacuum. if your wire is in a vacuum ofcourse Commented Nov 29, 2021 at 15:03

As long as $$I$$ is defined as TOTAL CURRENT through your wire (be it multi-strand or not) the expression shouldn't change. For example, if you have 5A current flowing through "normal" wire the field will be the same as for 5-strand wire where current of 1A is flowing through each strand. Btw, "B=\mu_0 \frac{N}{l}I" is how you would write your equation (you would only have to replace " with $). This equation gives an approximation of the magnetic of the magnetic inside a solenoid. This equation relates the current to the magnetic field. if you were to run the same current about a wire made of a different material, nothing would change. however the answer I think you are looking for, is that in real life, to MAKE a current, you need to apply a potential difference across the wire. If you were to run the same PD across multiple wires, they would give you different currents If they follow ohms law, the I= V/R • So, if we had to apply the same PD to a normal wire and a multi-strand one, the last one should allow a larger current to flow due to his lower resistance, therefore increasing the magnetic field, right? – Phys Commented Nov 29, 2021 at 16:58 • @Phys Correct, although multi-strand wire would have lower resistance only if its total cross-section is larger than for normal wire (assuming we use same materials). One wire with cross-section$S$has the same resistance as 5-strand wire each with cross-section$S/5\$ (you can verify that yourself). More complications arise if you use high frequency voltage source in which case resistance of multi-strand wire would be higher due to skin effect (basically for high frequencies current through a conductor is concentrated on its thin surface layer, lowering the effective cross-section). Commented Nov 29, 2021 at 19:01