Question

A metallic rod of length l is tied to a string of length 2l and made to rotate angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field B in the region, the emf induced across the ends of the rod is

• A. $\frac{7B\omega l^2}{2}$
• B. $\frac{3B\omega l^2}{2}$
• C. $\frac{5B\omega l^2}{2}$
• D. $\frac{4B\omega l^2}{2}$

Answer 1

The correct option is C

$\frac{5B\omega l^2}{2}$

$e=\frac{d\varphi }{dt}=\frac{BdA}{dt}=\frac{B\pi \left[\right(3l{)}^2-\left(2l{)}^2\right]}{\frac{1}{n}}\times B\pi n\times 5I^{2}e=B\left(2\pi n\right)\times \frac{5}{2}{I}^2=-\frac{5}{2}B\omega I^2$