Homopolar generator
= Homopolar generator
{title2=$\mathcal E=\omega Ba^2/2$}
For a conducting disc of radius $a$ rotating in a uniform axial <magnetic field> $B$, the shaft-to-rim <motional electromotive force> is $\int_0^a\omega rB\,dr=\omega Ba^2/2$. A current $I$ between shaft and rim gives the opposing <torque> $IBa^2/2$, making electromagnetic conversion <power> $\mathcal E I$ equal to mechanical <torque> times <angular speed>.