Question

A unicycle has 200 turns of thin wire wrapped around its rim, creating loops with the same

diameter as the wheel. An emf of 9V is induced when the wheel is perpendicular to a magnetic

field that steadily decreases from 0.68 T to 0.24 T in 10 seconds. What is the radius of the

wheel?

Answer 1

$\xi=-n\frac{d\Phi}{dt}=-Sn\frac{dB}{dt}=-\pi r^2 n\frac{dB}{dt},\implies$

$r=\sqrt{-\frac{\xi dt}{\pi n dB}},$

$r=\sqrt{-\frac{9\cdot 10}{3.14\cdot 200\cdot(0.24-0.68)}}=1.8~m.$