A metallic ring of mass 2kg and radius 1m with a uniform metallic spoke of same mass 2kg and length 1m is rotated about its axis with angular velocity 1 rev/sec. in a perpendicular uniform magnetic field B of magnitude 10T as shown in figure. If the central end of the spoke is connected to the rim of the wheel through a resistor R magnitude πΩ as shown. The resistor does not rotate, its one end is always at the center of the ring and other end is always in contact with ring. A force F ( In newton) as shown is needed to maintain constant angular velocity of the spoke then, fill F25 ( The ring and the spoke has zero resistance)

Question

A metallic ring of mass 2kg and radius 1m with a uniform metallic spoke of same mass 2kg and length 1m is rotated about its axis with angular velocity 1 rev/sec. in a perpendicular uniform magnetic field B of magnitude 10T as shown in figure. If the central end of the spoke is connected to the rim of the wheel through a resistor R magnitude πΩ  as shown. The resistor does not rotate, its one end is always at the center of the ring and other end is always in contact with ring. A force F ( In newton) as shown is needed to maintain constant angular velocity of the spoke then, fill  F25 ( The ring and the spoke has zero resistance)

Accepted Answer

Fb=BIL.(∴L=r=1m)Induced current:  I=(Bωr2/2)R ∴        Fb=B(Bωr22R)r=B2ωr32RTo maintain constant angular velocity:  F(r)=FB(r/2)⇒              F=FB2=B2ωr34R=(10)2×2π×(1)34×π=50N

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