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Two parallel rails are separated by l = 0.5 m. A conducting bar slides along them at a constant speed v = 10 m/s. At the left end, two capacitors C1 and C2 are connected in series with C2 = 1.5*C1. The whole arrangement is in a uniform magnetic field perpendicular to its plane. If the voltage across C2 is 0.5 V, find the magnitude of the magnetic field.
- 0.5 T
- 0.25 T
- 0.125 T
- 1 T
Correct answer: 0.25 T
Solution
The moving bar acts as a source of emf = B*l*v across the series combination. Since series capacitors carry equal charge, V2 = emf * C1/(C1 + C2) = emf/2.5 = 0.4*emf. Setting V2 = 0.5 V gives emf = 1.25 V, and B = emf/(l*v) = 0.25 T.
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