A conducting rod of length l is hinged at point O. It is a free to rotate in a verical plane. There exists a uniform magnetic field B in horizontal direction. The rod is released from the position shown. The potential difference between the two ends of the rod is proportional to

Options

A. `l^(3//2)`
B. `l^(2)`
C. `sintheta//2`
D. `sin theta`

Explanation

`mg(l//2)sintheta=(1)/(2)xx(ml^(2))/(3)omega^(2)`
`omega=sqrt((3gsintheta)/(l))`
Potential difference induced between two ends of the rod `=epsilon=(1)/(2)Bomegal^(2)`
`epsilon=(1)/(2)Bl^(3//2)sqrt(3gsintheta )`