A long straight wire carries a current, I $$=$$ $$2$$ ampere. A $$semi-circular$$ conducting rod is placed beside it on two consuding parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the $$semi-circular$$ rod are at distances $$1$$ cm $$and4$$ cm from the wire. At time t $$=$$ $$0$$, the rod starts moving on the rails with a speed v $$=$$ $$3.0$$ $$m/s$$ (see$$ the $$figure).A resistor $$R=1.4$$Ω and a capacitor $$C0=5.0$$μF are connected in series between the rails.At time t $$=$$ $$0$$, $$C0$$ is uncharged. Which of the following $$statement(s)$$ $$is(are)$$ correct ?μ$$0=4$$π×$$10$$−$$7$$ SI units. Take ln⁡$$2=0.7$$

Question

A long straight wire carries a current, I $$=$$ $$2$$ ampere. A $$semi-circular$$ conducting rod is placed beside it on two consuding parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the $$semi-circular$$ rod are at distances $$1$$ cm $$and4$$ cm from the wire. At time t $$=$$ $$0$$, the rod starts moving on the rails with a speed v $$=$$ $$3.0$$ $$m/s$$ (see$$ the $$figure).A resistor $$R=1.4$$Ω and a capacitor $$C0=5.0$$μF are connected in series between the rails.At time t $$=$$ $$0$$, $$C0$$ is uncharged. Which of the following $$statement(s)$$ $$is(are)$$ correct ?μ$$0=4$$π×$$10$$−$$7$$ SI units. Take ln⁡$$2=0.7$$

Infinity Learn · Accepted Answer

→ Here V is instantaneous velocityEmf⁡$$AB=$$∫(V$$¯×B¯$$)⋅dx $$=V$$∫μ$$0i2$$$$π$$xdxε$$=$$μ$$0iV2$$$$π$$ln⁡(4)ε−$$i1R=qC$$⇒$$i1=dqdt$$ ……..(i)ε$$=$$μ$$0i2$$π$$($$ℓ$$n4)(V)$$ For maximum charge $$dqdt=i1=0$$ From (1) ε$$=qCImax=$$μ$$0iV2$$$$π$$ln⁡(4)×$$C0=8.4$$×$$10$$−$$12CFor$$ maximum current q $$=$$ $$0$$⇒ $$i1=$$εR;μ$$0iV2$$$$π$$ln⁡$$(4)R=1.2$$×$$10$$−$$6Amp$$

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