= Electrical generator
An <electrical generator> converts mechanical work into electrical <energy>. In an induction generator, relative motion changes how a conducting circuit interacts with a <magnetic field>. For an ideal coil with $N$ turns and area $A$, rotating at <angular velocity> $\omega$ in a uniform field of magnitude $B$, the linked <magnetic flux> is $NBA\cos\omega t$. <Faraday's law> gives the <electromotive force>
$$
\mathcal E(t)=NBA\omega\sin\omega t,
$$
with sign determined by the chosen loop orientation. Connecting a load lets this <electromotive force> drive an <electric current>; the resulting electromagnetic torque opposes the driving motion, consistent with <conservation of energy>.
<Michael Faraday>'s rotating-disc apparatus makes the conversion visible without a many-turn coil. A copper disc rotated between magnetic poles, with an external circuit contacting its axle and rim. The motion-dependent <Lorentz force> separates charge between those contacts. This <homopolar generator> maintains one output polarity for a fixed field and rotation direction, unlike the alternating output of the rotating-coil example.<Experimental Researches in Electricity, Volume 1 by Michael Faraday>[First Series, §4, paragraphs 85–100: rotating copper disc, conducting contacts, galvanometer and reversal tests]{ref}
An original quantitative demonstration compares the open-circuit output at different rotation rates while retaining the same coil and field geometry. The ideal prediction is proportionality to $\omega$. Under load, losses and the required driving torque supply additional tests of the conversion model.
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