A conducting rod AC of length $$4l$$ is rotated about a point O in a uniform magnetic field B→ directed into the paper. AO $$=$$ l and OC $$=$$ $$3l$$. Then

Correct option is 3VA−VC=4Bωl2

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A conducting rod AC of length 4l is rotated about a point O in a uniform magnetic field $\vec{B}$ directed into the paper. AO = l and OC = 3l. Then

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VA−VO=Bωl22

VO−VC=72Bωl2

VA−VC=4Bωl2

VC−VO=92Bωl2

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detailed solution

Correct option is C

By using e=12Bl2ωFor part AO ; eOA=eO−eA=12Bl2ωFor part OC; eOC=eO−eC=12B(3l)2ω∴eA−eC=4 Bl2ω

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The diagram shows a circuit having a coil of resistance $R = 2.5 Ω$ and inductance L connected to a conducting rod PQ which can slide on a perfectly conducting circular ring of radius 10 cm with its centre at 'P'. Assume that friction and gravity are absent and a constant uniform magnetic field of 5 T exists as shown in figure.

At t = 0, the circuit is switched on and simultaneously a time varying external torque is applied on the rod so that it rotates about P with a constant angular velocity 40 rad/s. Find magnitude of this torque (in milli Nm) when current reaches half of its maximum value. Neglect the self-inductance of the loop formed by the circuit.

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