Question

An infinitely long wire has a current i, as shown, where io is a known constant. Above the wire, a rod of mass m and resistance R slides without friction on resistance-free rails, which are in turn connected to a capacitor of capacitance C. At t = 0, the rod is a distance of L from the capacitor. Batman pushes on the rod to ensure that it moves at a constant velocity Vo. Ignore the self-inductance of the circuit. L VO с W a y zex Out of Page lo Assuming dŚ still points out of the page, and that the magnetic flux you found in a) is given by at, find the charge on the capacitor as a function of time.

Answer 1

solution dr W с Resistance R The cussent cassying meire will produce a magnelie field ginen B = lo Io (k) (at distance & from the 2ar rod) - This is the magnetic field due to infinite noire Direction is dix Derection of 6 = ginen = îx} = k Neue, as the hod is morning with constant speed to so the flux through the loop will change. sue to change in flux enf will be present in the circuit ( By Faraday's electromagnetic induction) lane of

euf S B x W) de across I ends of the Rod is euf as- given I (BxW). U (lo Jo XX. Vo?) dr↑ (frem. D) ulio Iove (de (x2) zar atw 20 au lio Io la lu&atw 은 emf sue to this eny current will flow through the Molovo enatw 27 circuit dime, ko is in te direction, that means flees in cseases thers leurs dans duestion of cusent should be such So cursent will be in clockwise direction of rod I s euf due to movement. given by eq ® Resistance of lod C I &R

Newe, apply Kirchoffe Voltage low in the circuit - V+ IRt Ve=0 he know Q = CV Ve=Q C and I do at. so, Ve vet IR V= a + do R c dt do R c dt CV-Q = dt do (RC) t da I felt Jev-a RC o 0 7- en LCV-A) I() Rc = (CV-Q) = é 4 RC CV e ERC CV falt). cv [ 1- e-tRc]

where = do lovo in/atw 27 ܩܫܲܦܐܚܐ w So, this gives the vastation of charge through capacitor