A metal rod of length , moving with an angular velocity `omega` and velocity of its centre is v. Find potential difference between points A and B at the instant shown in figure. A uniform magnetic field of strength B exist perpendicular to plane of paper

Options

A. `Bvl`
B. `Bvl+1/2 B omegal^(2)`
C. `Bometal-1/2Bomegal^(2)`
D. `Bvl +Bomega(l/2)^(2)`

Explanation

Point P is at instantaneous rest,
`epsilon_(1)=|v_(P)-v_(A)|=1/2 B omega(l/2+v/(omega))^(2)`
`epsilon_(2)=|v_(P)-v_(B)|=1/2 B omega(l/2-v/(omega))^(2)`
`|v_(A)-v_(B)|=epsilon_(1)-epsilon_(2)`
`|v_(A)-v_(B)|=B l v`