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

Question

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

Infinity Learn · Accepted Answer

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

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