A metallic ring of mass 2 kg and radius 1 m with a uniform metallic spoke of same mass 2 kg and length 1 m is rotated about its axis with angular velocity 1 rev sec - 1 . In a perpendicular uniform ma

Question

A metallic ring of mass 2 kg and radius 1 m with a uniform metallic spoke of same mass 2 kg and length 1 m is rotated about its axis with angular velocity 1 rev sec - 1 . In a perpendicular uniform magnetic field B of magnitude 10 T as shown in the figure. If the central end of the spoke is connected to the rim of the wheel through a resistor R of magnitude π Ω as shown. The resistor does not rotate, it's one end is always at the centre of the ring and another end is always in contact with the ring. A force F as shown is needed to maintain the constant angular velocity of the spoke then, F is equal to (The ring and the spoke has zero resistance)

TestHub · Accepted Answer

F b = B I L Induced current: I = B ω r 2 2 R ∴ F B = B B ω r 2 2 R r = B 2 ω r 3 2 R To maintain constant angular velocity: F r = F B r 2 ⇒ F = F B 2 = B 2 ω r 3 4 R = 10 2 × 2 π × 1 3 4 × π = 50 N

Physics - EMI/AC Question with Solution | TestHub

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