A square loop of side 10 cm, free to rotate about a vertical axis c...

Question

A square loop of side 10 cm, free to rotate about a vertical axis coinciding with its one arm, is initially held perpendicular to a uniform horizontal magnetic field of 0.2 T. If it is rotated at the uniform speed of 60 rpm, find the emf induced in the loop.

Accepted Answer

Side $=10$ cm $=0.1$ m, Area $A=0.01	ext{ m}^2$, $B=0.2$ T, rotating at $60$ rpm. $$\omega=60	ext{ rpm}=\frac{60	imes2\pi}{60}=2\pi	ext{ rad/s}\approx6.283	ext{ rad/s}$$ Peak emf (standard rotating-coil formula, $N=1$): $$\varepsilon_0=BA\omega=0.2	imes0.01	imes6.283\approx1.257	imes10^{-2}	ext{ V}\approx12.6	ext{ mV}$$

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