A uniform but time varying magnetic field is present in a circular region of radius R. The magnetic field is perpendicular and into the plane of the loop and the magnitude of field is increasing at a constant rate `alpha`. There is a straight conducting rod of length 2R placed as shown in figure.

The magnitude of induced emf across the rod is

Options

A. `piR^(2)alpha`
B. `(piR^(2)alpha)/(2)`
C. `(R^(2)alpha)/(sqrt2)`
D. `(Pir^(2)alpha)/(4)`

Answer

D

Explanation

Induced emf, `V_(BA)=int E.dl=(1)/(4)((dphi)/(dt))`

`=(1)/(4)(piR^(2)).(dB)/(dt)=(piR^(2)alpha)/(4)" "[thereforephi=B.Aand (dB)/(dt)=alpha]`