Solve this:

Solve this: 2 A rod of mass m is lying on a rail as shown in figure. Initially the rod is at rest. Length of rod is J and resistance in the circuit is R If a constant force F applied on the rod. find expression for velocity of rod as a function of time.

Let velocity at any instant of the rod is v . Let a magnetic field is directed into the page.Emf induced in the rod is E=Bvl (with positive polarity upwards)current in the circuit is i=ER=Bvl RMagnetic force on the rod is Fmag=BilFmag=B× Bvl R×l=B2vl2RNet force on the rodFnet=F-B2vl2Rma=F-B2vl2Rma=F-B2vl2mRmdvdt=F-B2vl2R0vmdvF-B2vl2R=0tdt-mRB2l2(ln(F-B2vl2R)v0=tln(F-B2vl2R)-ln(F)=-B2l2tmRln(F-B2vl2RF)=-B2l2tmRln(1-B2vl2FR)=-B2l2tmR(1-B2vl2FR)=e-B2l2tmRv=FRB2l2(1-e-B2l2tmR)RegardsDear student
 

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