A metal rod of mass m = 100 g and length L = 1.0 m rests on two fixed, friction

Question

A metal rod of mass m = 100 g and length L = 1.0 m rests on two fixed, friction less, conducting rails, as seen from above in the diagram. Switch S is closed at time t = 0, allowing the battery V_b = 50 V to generate current through the top rail, down through the rod, and then through the other rail back to the battery. The wires have a combined resistance R = 2ohm and they are immersed in a uniform magnetic field of strength B = 0.02 T pointing downward (as shown). 4) What is the current in the circuit at time t = 2.0 s? 5) What is the force on the rod for time t > 0? 6) What is the velocity of the rod at time t = 2.0 s?

Explanation / Answer

4) current i = V/R = 50/2 = 25 A

5) force F = B*i*L = 0.02*25*1 = 0.5 N

6) but emf V = B*L*v = 50

v = 50 /(B*L) = 50 /0.02 = 2.5 km/sec = 2.5*10^3 m/sec

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