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 removed
at a certain point P. What distance (in x 10² m) does the conducting wire cover on rails from point P before stopping?
$(Given: F_{0} = 20 N, m = 1.0 gm, R = 0.01 Ω, l = 10 cm, B=0.1T)$

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 removed
at a certain point P. What distance (in x 10² m) does the conducting wire cover on rails from point P before stopping?

$(Given: F_{0} = 20 N, m = 1.0 gm, R = 0.01 Ω, l = 10 cm, B=0.1T)$

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⇒$$v0=B2l2mRss=mRv0B2l2=F0mR2B4l4=200m$$

Magnetic flux and induced emf

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Magnetic flux and induced emf

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For constant velocity, A=0F0=Fm=ilB=εRlB=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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