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

Question

A metal rod of mass m = 100 g and length L = 1.0 m rests on two fixed, frictionless, 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 = 2 Ohm and they are immersed in a uniform magnetic field of strength B = 0.02 T pointing downward (as shown). What is the current in the circuit at time t = 2.0 s? What is the force on the rod for time t > 0? What is the velocity of the rod at time t = 2.0 s?

Explanation / Answer

(4)
V = I*R
I = V/R
I = 50.0 / 2
I = 25.0 A

(5)
F = I*L*B
F = 25 * 1.0 * 0.02
F = 0.5 N

(6)
F = m*a
a = 0.5/(0.1)
a = 5.0 m/s^2

v = u + a*t
v = 0 + 5.0 * 2
v = 10.0 m/s

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