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

Options

A. (a) `l^(3//2)`
B. (b) `l^(2)`
C. (c ) `sin theta`
D. (d) `(sin theta)^(1//2)`

Answer

B, D

Explanation

(b, d): Potential difference `= (1)/(2) Bomegal^(2)`
From energy conservation: `mg = (l)/(2)sin theta = (1)/(2)Iomega^(2),` where `I = (ml^(2))/(3)`
`rarr` `omega prop (sin theta)^(1//2)` `rarr` e alpha omega` `rarr` `e prop (sin theta)^(1//2)`
also `e prop l^(2)`