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A wire cd of length l and mass m is slid...

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

A

`(mgR)/(Bl)`

B

`(mgR)/(B^(2)l^(2))`

C

`(mgR)/(B^(3)l^(3))`

D

`(mgR)/(B^(2)l)`

Text Solution

Verified by Experts

The correct Answer is:
B
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))`.
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