The endpoints of a conducting string (shaped as a circular loop) of constant length are being pulled at a constant velocity v as shown in the figure. There exists a uniform magnetic field B is space which is perpendicular to the circular loop. If the loop always remains circular during the motion of its endpoints, them the emf induced in the loop at `t=(piR)/(2v)` is

Options

A. 2BRv
B. BRv
C. 4BRv
D. 0.5 BRv

Answer

B

Explanation

At any instant, the radius of the loop r, will satisfy the following relation:
`2pir + 2vt = 2piR`
`rArr r = R- (vt)/pi`
The flux of the magnetic field at any instant, will be:
`phi_(B) = pir^(2)B`
So, the induced emf is:
`E = |-(dphi)/(dt)| = 2piBr(dr)/(dt)`
`rArr E = 2piB (R - (vt)/pi)v`
`rArr E = BRv`