A circular conducting loop of radius `r_(0)` and having resistance per unit length `lambda` as shown in the figure is placed in a magnetic field B which is constant in space and time. The ends of the loop are crossed and pulled in opposite directions with a velocity v such that the loop always remains circular and the radius of the loop goes on decreasing, then

Options

A. radius of the loop changes with r as `r=r_(0)-(v t)/(pi)`
B. emf induced in the loop as a function of time is `epsilon = 2B v [r_(0)-(v t)/(pi)]`
C. current induced in the loop is `I=(Bv)/(2pi lambda)`
D. current induced in the loop is `I=(Bv)/(pi lambda)`.

Answer

A, B, D

Explanation

Perimeter is decreasing at a rate of 2v
`therefore (d)/(dt)(2pi r)=2v " " therefore (dr)/(dt)=(v)/(pi)`
`therefore r=(r_(0)-(v)/(pi)t)` and `phi=B. pi r^(2)`
`rArr epsilon = |(-d phi)/(dt)|=B. 2pi. r(dr)/(dt)`
`therefore epsilon=2B pi(r_(0)-(v)/(pi)t)(v)/(pi)=2Bv (r_(0)-(v)/(pi)t)`
`therefore I=(phi)/(R )=(2B br)/(lambda.2pi r)=(Bv)/(pi lambda)`