Question

A wire shaped as a circle of radius R rotates about the axis OO' with an angular velocity $\omega$ as shown in figure. Resistance of the circuit is $R$. Find the mean thermal power generated in the loop during a period of a rotation.

• A. $\frac{(B\pi a^2\omega {)}^2}{4R}$
• B. $\frac{(B\pi a^2\omega {)}^2}{2R}$
• C. $\frac{(3B\pi a^2\omega {)}^2}{2R}$
• D. None of these

Answer 1

Answer: (B)

$\frac{(B\pi a^2\omega {)}^2}{2R}$

$A=\pi a^2\cos \omega t;\varphi =BA=B\pi a^2\cos \omega t$
$i=\frac{\epsilon }{R}=-\frac{d\varphi }{dt}/R=\frac{B\pi a^2\omega \sin \omega t}{R}$ and

$<P>=\frac{1}{T}{\int }_0^T{i}^{2}Rdt=\frac{(B\pi a^2\omega {)}^2}{2R}$