The magnetic field in a solenoid of length $L$ around an iron core with $N$ turns is given by: $$ B = \mu \frac{NI}{L}.$$. Assuming some Ohm's law type of resistance in the wire we can replace $I$ with $V/R$ to get $$ B = \mu \frac{NV}{LR}.$$. So the magnetic field strength increases linearly with both the number of turns and the voltage. The resistance of a wire is given by. $$ R = \rho \frac{l}{A}, $$.(where $\rho$ is some material property of the wire, $A$ is the cross sectional area and $l$ is the length) so that $LR = \rho Ll/A$ and.ssuming some Ohm's law type of resistance in the wire we can replace $I$ with $V/R$ to get $$ B = \mu \frac{NV}{LR}. $$. So the magnetic field strength increases linearly with both the number of turns and the voltage. The resistance of a wire is given by. $$ R = \rho \frac{l}{A}, $$.
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