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Two vertical conducting rails 1 m apart are joined at their ends by resistors R1 and R2. A horizontal conducting bar of mass 0.2 kg slides down the rails without friction under gravity. A uniform horizontal magnetic field of 0.6 T acts perpendicular to the plane of the rails. At terminal velocity the powers dissipated in R1 and R2 are 0.76 W and 1.2 W respectively. Find the terminal velocity of the bar.

1. about 1 m/s
2. about 1.6 m/s
3. about 3.3 m/s
4. about 0.5 m/s

Correct answer: about 1 m/s

Solution

At terminal velocity the net force is zero, so all the gravitational power mgv is converted to electrical power dissipated in the two resistors: mgv = P1 + P2 = 0.76 + 1.2 = 1.96 W. With m = 0.2 kg and g = 9.8, v = 1.96/(0.2*9.8) = 1.96/1.96 = 1.0 m/s. Using g=10, v=0.98 m/s. So terminal velocity ~ 1 m/s.

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