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A metal rod of resistance 20 ohm is fixed along a diameter of a conducting ring of radius 0.1 m lying in the xy-plane, in a uniform magnetic field B = 50 T along the z-axis. The ring (with the rod) rotates about its central axis at omega = 20 rad/s. An external resistance of 10 ohm is connected between the ring's centre and its rim. Find the current through the external resistance.
- 0.33 A
- 0.50 A
- 1.0 A
- 0.25 A
Correct answer: 0.33 A
Solution
Each half of the rod is a radial conductor from centre to rim of length R = 0.1 m, generating emf = (1/2)*B*omega*R² = 0.5*50*20*(0.1)² = 5 V. The rod's 20 ohm splits into two 10 ohm halves; the two halves act as two identical 5 V cells with 10 ohm internal resistance connected in parallel. The parallel combination gives emf 5 V with internal resistance 5 ohm. With the 10 ohm external resistor: I = 5/(5+10) = 1/3 = 0.33 A.
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