A horizontal wire is free to slide on the vertical rails of a conducting frame as shown in figure. The wire has a mass `m` and length `l` and the resistance of the circuit is `R`. If a uniform magnetic field `B` is directed perpendicular to the frame, the terminal speed of the wire as it falls under the force of gravity is

Options

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

Answer

D

Explanation

net force on the wire is zero when termional speed is attained.
`:. F_(m)=mg`
or `ilB=mg`
or `((e)/(R ))lB=mg`
or `((BvTl)/(R ))lB=mg(v_(T)="terminal speed")`
or `v_(T)=(mgR)/(B^(2)l^(2))`.