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 magnetic field, wire will experience an upward
force `F=Bil=B((Bvl)/(R ))l` `impliesF=(B^(b)vl^(2))/(R )`
if wire slides down with constant velocity then
`F=mgimplies(B^(2)vl^(2))/(R )=magimpliesv=(mgR)/(B^(2)l^(2))`