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More turns -> stronger field
more turns -> longer copper wire
longer copper wire -> more resistance(ohm)

at what turn does the resistance make the electromagnet weaker? - I want to make an ideal electromagnet.

(Sorry for being vague but I'm looking for some kind of formula or an example)

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up vote 1 down vote accepted

You need to combine some equations, lets list them:

Whe asume that you want the formula in terms of potential diferential, with Ohm's Law, $\Delta V = I R$, and the magnetic field inside one solenoid:

$$ B = \frac{N}{L}\mu I = \frac{N}{L}\mu \frac{\Delta V}{R} \quad\quad (1) $$

where $N$ , $L$, $\mu$, stand for the number of turns, lenght of the solenoid and magnetic permeability of you core respectively. Then we also know the dependance of $R$ over the lenght of the wire, $R = \rho\frac{l}{A}$, where $\rho$ is the resistivity, $A$ the cross section of the wire and $l$ the lenght. We can compute the lenght by:

$$ l = 2\pi rN $$

so if we subtitute the last equations in $(1)$:

$$ B = \mu\frac{N\Delta V}{L}\frac{A}{\rho 2 \pi r N } = \mu\frac{\Delta V A}{2 \pi \rho r L} $$

surprisingly it doesn't care the number of turns!!

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