Question

Problem 8 A conducting rod with mass m slides down two conducting rod, as shown in figure (22.53). (i) Determine the direction of the induced current. (ii) Determine the speed of the rod after it has fallen for a long period of time. 322CHAPTER 22. ELECTROMAGNETIC INDUCTION AND FARADAY'S LAW Figure 22.53: Problem 8

Answer 1

Ans-

i)-The direction of induced current can be determined by Lenz Law.It states that current is induced in such a way that it opposes the change in magnetic flux.Since the magnetic flux due to inside the plane magnetic field is increasing hence current must be induced in such a way that it produces a magnetic field outside the plane.Hence the current must be in counterclockwise direction.

ii)-When the rod has fallen for a long time then it moves with constant velocity 'v'.

So work done =W

W=F.s

=m.g.v.t (Here m is the mass of rod,g is acceleration due to gravity,v is the constant velocity ,t is time for which it has fallen) -----------------(1)

Also work done is given by

W=V^2*R/t (Here V is the induced emf)----------------------(2)

Induced emf is given as V=B*l*v*t (since B is perpendicular to v so sine component is 1)'

Substituting V in (2) we get

W = B ² L ² V ² t /R-------------------(3)

Equating (1) and (3) we get

  V =  m*g*R / B ² L ²

This the required answer.