Magnetic field in the cylindrical regaion with its axis passing through O varies at a constant rate `(dB)/(dt)`. A treangular imaginary loop ABC, with `AB = BC`, is lying in this region as shown in the adjacent figure. The work done to move unit positive charge from A to B along the side AB is

Options

A. `r^(2)(dB)/(dt)`
B. `pir^(2)(dB)/(dt)`
C. `(r^(2))/(2)(dB)/(dt)`
D. `(3r^(2))/(4)(dB)/(dt)`

Answer

C

Explanation

No e.m.f. will be induced in AC because electric lines of force are perpendicular to AC and e.m.f. induced in `AB=` e.m.f. induced in BC.
`:.` e.m.f. induced in `AB=(1)/(2)|(dphi)/(dt)|=(1)/(2)r^(2)(dB)/(dt)`