A horizontal wire rod is free to slide on a vertical conducting frame as shown i

Question

A horizontal wire rod is free to slide on a vertical conducting frame as shown in the figure. The wire has mass 6 kg and length 8 m. It maintains good contact with the conducting frame. The resistance of the circuit is 2 ?. A uniform magnetic field with magnitude 6 T is directed perpendicular to the frame (out of the page).

A) The wire will accelerate downward until the upward force on the wire (due to the interaction of the current with the magnetic field) balances the gravitational force. Neglecting frictional effects, find the terminal velocity of the wire. Answer in units of m/s

B) Find the current induced in the wire if the wire is falling with a terminal speed v?. Answer in units of A.

Explanation / Answer

Let v is the terminal speed.

a) induced emf when it the wire is falling with terminal speed, emf = B*v*L

= 6*v*8

= 48*v

induced current, I = emf/R

= 48*v/2

= 24*v

magnetic force acting on the rod, FB = B*I*L

= 6*24*v*8

= 1152*v

when the rod falls with terminal speed, FB = Fg

1152*v = m*g

v = m*g/1152

= 6*9.8/1152

= 0.051 m/s

B) Induced current = 24*v

= 24*0.051

= 1.225 A

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