Question

A wire of length l, mass m and resistance R slides without any friction down the parallel conducting rails of negligible resistance (Fig 3.126). The rails are connected to each other at the bottom by a resistanceless rail parallel to the wire so that the wire and the rails form a closed rectangular conducting loop. The plane of the rails makes an angle $\theta$ with the horizontal and a uniform vertical magnetic field of induction B exist throughout the region. Find the steady-state velocity of the wire.

• A. $mgsin\theta$
• B. $\frac{mg}{R}\frac{{\sin }^2\theta }{B^2{l}^2{\cos }^2\theta }$
• C. $\frac{mgR\sin \theta }{B^2{l}^2{\cos }^2\theta }$
• D. $mgr\frac{{\sin }^2\theta }{B^2{l}^2\cos \theta }$

Answer 1

Answer: (A)

$mgsin\theta$

$i=\frac{BLV}{R}=\frac{b\left(l\cos \theta \right)\left(v\cos \theta \right)}{R}$
$F=iLB=\frac{BLV{\cos }^2\theta LB}{R}$
$F=mg\sin \theta$