A $$non-conducting$$ $$non-magnetic$$ rod having circular cross section of radius R is suspended from a rigid support as shown in the figure. A light and small coil of $$300$$ turns is wrapped tightly at the left end of the rod where uniform magnetic field B exists in vertically downward direction.Air of density ρ hits the half of the right part of the rod with velocity V as shown in the figure. What should be current in clockwise direction (as$$ seen from $$O) in the coil so that rod remains horizontal? Give answer in m A. $$Given2Lv$$$$π$$RBρ$$=15$$ $$A-1/2$$

Question

A $$non-conducting$$ $$non-magnetic$$ rod having circular cross section of radius R is suspended from a rigid support as shown in the figure. A light and small coil of $$300$$ turns is wrapped tightly at the left end of the rod where uniform magnetic field B exists in vertically downward direction.Air of density ρ hits the half of the right part of the rod with velocity V as shown in the figure. What should be current in clockwise direction (as$$ seen from $$O) in the coil so that rod remains horizontal? Give answer in m A. $$Given2Lv$$$$π$$RBρ$$=15$$ $$A-1/2$$

Infinity Learn · Accepted Answer

Force exerted by air on the rod $$=$$ρ$$L22Rv2=$$ρ$$LRv2$$  Balancing torque about point O,NI$$π$$$$R2B=$$ρ$$LRv23L4$$ ⇒  $$300$$$$π$$$$IBR=3$$ρ$$v2L24$$ ⇒  $$I=$$ρ$$L2v2400$$$$π$$$$BR=1100Lv2$$ρπ$$BR2=0.002$$ $$A=2$$ mA

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