Two long, horizontal pair of rails shown in the figure is connected using resistance R. The distance between the rails is l, the electrical resistance of the rails is negligible.A conducting wire of mass m and length l can slide without friction on the pair of rails, in a vertical, homogeneous magnetic field of induction B.A force of magnitude $$F0$$ is exerted for sufficiently long time onto the conducting wire, so that the speed of the wire becomes nearly constant. The force $$F0$$ is now removedat a certain point P. What distance (in$$ x $$102$$ $$m) does the conducting wire cover on rails from point P before stopping? (Given$$: $$F0=20N$$,$$m=1.0gm$$,$$R=0.01$$Ω,$$l=10cm$$, $$B=0.1T)

Question

Two long, horizontal pair of rails shown in the figure is connected using resistance R. The distance between the rails is l, the electrical resistance of the rails is negligible.A conducting wire of mass m and length l can slide without friction on the pair of rails, in a vertical, homogeneous magnetic field of induction B.A force of magnitude $$F0$$ is exerted for sufficiently long time onto the conducting wire, so that the speed of the wire becomes nearly constant. The force $$F0$$ is now removedat a certain point P. What distance (in$$ x $$102$$ $$m) does the conducting wire cover on rails from point P before stopping? (Given$$: $$F0=20N$$,$$m=1.0gm$$,$$R=0.01$$Ω,$$l=10cm$$, $$B=0.1T)

Infinity Learn · Accepted Answer

For constant velocity, $$A=0F0=Fm=ilB=$$ε$$RlB=Blv0RlBv0=F0RB2l2$$ gives velocity at point 'P'  Now, retardation $$a=Fmm=ilBma=B2l2mRv$$⇒−$$vdvds=B2l2mRv$$−∫$$v00$$ $$dv=B2l2mR$$∫$$0s$$ ds⇒$$v0=B2l2mRss=mRv0B2l2=F0mR2B4l4=200m$$

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