Question

A wire cd of length l and mass m is sliding without friction on conducting rails ax and by as shown. The vertical 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. $\frac{mgR}{Bl}$
  
• B. $\frac{mgR}{B^2{l}^2}$
  
• C. $\frac{mgR}{B^3{l}^3}$
  
• D. $\frac{mgR}{B^{2}l}$

Answer 1

The correct option is B $\frac{mgR}{B^2{l}^2}$


Due to magnetic field, wire will experience an upward force $F=Bil=B\left(\frac{Bvl}{R}\right)l\Rightarrow F=\frac{B^{2}v{l}^2}{R}$
If wire slides down with constant velocity then
$F=mg\Rightarrow \frac{B^{2}v{l}^2}{R}=mg\Rightarrow v=\frac{mgR}{B^2{l}^2}$