A metal crossbar of mass m rides on a parallel pair of long horizontal conductin

Question

A metal crossbar of mass m rides on a parallel pair of long horizontal conducting rails separated by a distance L and connected to a device that supplies constant current I to the circuit, as shown below. The circuit is in a region with a uniform magnetic field whose direction is vertically downward. There is no friction and the bar starts from rest at t = 0.

(a) In which direction will the bar start to move?

(b) Show that at time t the bar has a speed of (BIL/m)t.

Explanation / Answer

a)

Using right hand rule , direction of force on the cross-bar comes out to be towards right. Hence the bar moves towards right.

b)

magnetic force is given as

F = i BL

from newton's second law

F = ma

so ma = iBL

a = iBL / m

Vi = initial velocity = 0 m/s

Vf = final velocity

t = time

using the equation

Vf = Vi + at

Vf = 0 + (iBLt/ m )

V = (iBLt/ m )

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