A square loop is placed in a uniform magnetic field `vecB` as shown in fig. The power needed to pull it out of the field with a velocity v is proportional to

Options

A. `v^(1//2)`
B. v
C. `v^2`
D. `v^(3//2)`

Answer

C

Explanation

(3)
If l is the side of the square loop, the magnitude of emf induced is `|e|=Blv`. If R is the resistance of the loop, the induced current is
`i=(Blv)/R`
The force required to pull the loop is
`F=Bil=(B^2l^2v)/R`
`:.` Power needed is `P=Fv=(B^2l^2v)/R`.