A circular conducting loop of radius `r_(0)` and having resistance per unit length lamba 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)-vt//pi`
B. EMF induced in the loop as a function of time is `e=2Nv[r_(0)-vt//pi]`
C. Current induced in the loop is `I=(Bv)/(2pilambda)`
D. Current induced in the loop is `I=(Bv)/(pilambda)`

Answer

A, B, D

Explanation

Perimeter is decreasing at a rate of 2v
`d/(dt)(2pir)=2v Rightarrow(dr)/(dt)=v/pi`
`:.r=(r_(0)-v/pit)`
`phi=Bpir^(2)Rightarrowvarepsilon=|(-dphi)/(dt)|=B 2pi r(dr)/(dt)`
`:.varepsilon=2Bpi(r_(0)-v/pit)v/pi=2Bv(r_(0)-v/pit)`
`I=phi/R=(2Bvr)/(lambda.2pir)=(Bv)/(pilambda)`