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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.

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

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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 $).

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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

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  • $\begingroup$ 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? $\endgroup$
    – Phys
    Commented Nov 29, 2021 at 16:58
  • $\begingroup$ @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). $\endgroup$
    – Dario Barišić
    Commented Nov 29, 2021 at 19:01

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