Question

A metallic rod of length $l$' is tied to a string of length $2l$ and made to rotate with 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 e.m.f. induced across the ends of the rod is:

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

Answer 1

The correct option is C $\frac{5B\omega l^2}{2}$

$de$ $=B\left(\omega x\right)\cdot dx$

$e=B\omega {\int }_{2L}^{3L}.x.dx$

$=\frac{5B\omega L^2}{2}$