A wire `cd` of length `l` and mass `m` is sliding without friction on conducting rails `ax` and by as shown. The verticle rails are connected to each other with a resistance `R` between `a` and `b`. A uniform magnetic field `B` is applied perpendicular to the plane `abcd` such that `cd` moves with a constant velocity of

Options

A. `(mgR)/(Bl)`
B. `(mgR)/(B^(2)l^(2))`
C. `(mgR)/(B^(3)l^(3))`
D. `(mgR)/(B^(2)l)`

Answer

B

Explanation

Due to B, force (upward)
`F=BIl=B((Blv)/R)l=(B^(2)l^(2)v)/R`
If slides with constant velocity -
Then, `(B^(2)l^(2)v)/R=mgrArrv=(mgR)/(B^(2)l^(2))`.