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Q.

A thin copper rod ABC is bent at point B as shown in figure. The bent rod is rotating with angular velocity ω=10 rad/s about an axis passing through A and perpendicular to the plane of the bent rod. There is a uniform magnetic field of induction B = 0.5 T perpendicular to the plane of the page then induced potential difference between end C and point B is

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a

40 volt

b

20 volt

c

125 volt

d

60 volt

answer is A.

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Detailed Solution

le=Distance between A and C =32+42m=5m∴ VC−VA=12 Bωle2  and  VB−VA=12Bω(AB)2Now (VB−VA)+(VC−VB)=(VC−VA)⇒(VC−VB)=12Bω[le2−(AB)2]=12×0.5×10×(52−32)V⇒VC−VB=40 volt
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