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 emf induced across the ends of the rod is

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

Answer 1

Answer: (D)

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

Answer 2

$e = \int \limits_{ 2 \, l }^{ 3 \, l } \, ( \omega \, x ) \, Bdx = B \omega \frac{ [ ( 3 \, l )^2 - ( 2 \, l)^2 ] }{ 2 }$
= $\frac{ 5 B \, l^2 \, \omega }{ 2 }$