Question

A conducting rod of mass M with negligible electrical resistance slides on a pair of frictionless, horizontal, parallel, conducting rails separated by a distance L. The two rails are connected by an electrical resistance of R. A uniform magnetic field B is directed vertically upward in the entire region. a. Looking from above, is the conventional current flowing cw or cow? b. Determine the current through the resistor. c. Find the force necessary to keep the rod moving at a constant speed.

Answer 1

Answer:

Explanation:

Given

mass of rod is M

Distance between rails is L

If the direction of magnetic field is directed upwards

If rod is moving right then,

Area enclosed is increasing therefore a Clockwise current will induce

and if rod is moving left then enclosed area is decreasing therefore an anticlockwise current will setup in the circuit

(b)Induced EMF will be

$E=BvL$

where v=velocity of rod

and current is $I=\frac{V}R}$

$I=\frac{BvL}{R}$

(c)Force necessary to move rod with constant velocity v is

$F_{net}=F-BIL=0$

$F=BIL$

$F=B\times \frac{BvL}{R}\times L$

$F=\frac{B^2L^2v}{R}$