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At t=0 the switch s of the adjacent network is closed. The connector has mass m, length l and resitanceR; it is free to move on the rails. The capacitance of the capacitor is C. It is initially uncharged and a uniform magnetic field exists into the plane of the paper. What is the charge on the capacitor after a long time??...........answer is EmC/( C 2 B 2 l 2 + m)..........please post the solution specially the portion wher velocity of the connector is substituted.


At t=0 the switch s of the adjacent network is closed. The connector has mass m, length  l and resitanceR; it is free to move on the rails. The capacitance of the capacitor is C. It is initially uncharged and a uniform magnetic field exists into the plane of the paper. What is the charge on the capacitor after a long time??...........answer is EmC/( C2B2l2 + m)..........please post the solution specially the portion wher  velocity of the connector is substituted.


Grade:11

1 Answers

ROSHAN MUJEEB
askIITians Faculty 829 Points
one year ago

Solution :
qC+Bvl=εqC+Bvl=ε
q=C(ε−Bvl)q=C(ε-Bvl)
Now,mdvdt=Bilmdvdt=Bil
mdv=Blidtmdv=Blidt
m∫v0dv=Bl∫q0dqm∫v0dv=Bl∫q0dq
mv=Blqmv=Blq
∴q=mvBl∴q=mvBl...(i)
From (i) and (ii)
mvBl=Cε−CBlvmvBl=Cε-CBlv
⇒v=CBlε(m+CB2l2)

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