= Electric motor
An <electric motor> converts electrical <energy> into mechanical <work>, usually rotation, through electromagnetic forces. For a coil with $N$ turns, area $A$ and <electric current> $I$ in a uniform <magnetic field> $B$, the <torque> magnitude is
$$
\tau=NIAB\sin\theta,
$$
where $\theta$ is the angle between the coil's normal and the <magnetic field>. Repeated rotation requires the current or effective field arrangement to keep supplying torque in the intended direction. Electrical input power must cover useful output plus losses.
A coil with $N=100$, $I=0.5\,\mathrm A$, $A=0.01\,\mathrm{m^2}$ and $B=0.2\,\mathrm T$ has maximum <torque> $0.1\,\mathrm{N\,m}$. At angular speed $\omega$, instantaneous mechanical <power> is $P=\tau\omega$; the maximum-torque value alone does not specify a motor's sustained output.
<Michael Faraday>'s 1821 rotation experiment made the conversion visible: a current-carrying wire moved around a fixed magnet while a pool of <Mercury> maintained electrical contact. The Royal Institution preserves his 1822 apparatus, consisting of a wire, glass vessel and fixed bar magnet connected through the conducting liquid. Continuous rotation, rather than a single deflection, established a route from steady <electric current> to repeated mechanical motion.<Michael Faraday's electric magnetic rotation apparatus by Royal Institution>[Collection description, 1821 discovery and surviving 1822 apparatus]{ref}
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