= Electromagnet
{title2=$B\simeq\mu_0NI/L$}
An <electromagnet> produces a <magnetic field> using an <electric current>. Winding an <electrical conductor> into a <coil> combines the fields from its turns; a long <solenoid> is an idealized example. Far from its ends, an air-core <solenoid> has approximately
$$
B=\mu_0\frac{N}{L}I,
$$
where $N$ turns carry <electric current> $I$ over <length> $L$. Reversing $I$ reverses the axial <magnetic field>. <The Feynman Lectures on Physics, Volume II by Richard Feynman and others>[Section II.13–5, magnetic field of a straight wire and solenoid]{ref}
A core with <ferromagnetism> can concentrate the <magnetic flux>, but its response depends on <magnetic saturation> and <magnetic hysteresis>. The constant-permeability air-core formula cannot simply be extrapolated to arbitrarily large core fields. A <magnetic compass> near a powered <coil> provides a qualitative test: switching or reversing the <electric current> changes the compass orientation.
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