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Two paraller long smooth conducting rails separated by a distance l are connected by a movable conducting connector of mass m. Terminals of the rails are connected by the resistor R and the capacitor C as shown in fig. A uniform magnetic field B perpendicular to the plane of the rail is switched on. The connector is dragged by a constant force F. Find the speed of the connector as a function of time if the force F is applied at t = 0. Also find the terminal velocity of the conductor.


Two paraller long smooth conducting rails separated by a distance l are
connected by a movable conducting connector of mass m. Terminals of the
rails are connected by the resistor R and the capacitor C as shown in
fig. A uniform magnetic field B perpendicular to the plane of the rail
is switched on. The connector is dragged by a constant force F. Find
the speed of the connector as a function of time if the force F is
applied at t = 0. Also find the terminal velocity of the conductor.


Grade:10

1 Answers

ROSHAN MUJEEB
askIITians Faculty 829 Points
3 years ago
Vab=Bvl,i1=BvlR,q=C(Bvl)Vab=Bvl,i1=BvlR,q=C(Bvl)
∴i2=dqdt=CBIdvdt∴i2=dqdt=CBIdvdt
Now,i=i1+i2=BvlR+CBIdvdti=i1+i2=BvlR+CBIdvdt
Magnetic forceFm=ilB=B2l2R.v+B2l2C.dvdtFm=ilB=B2l2R.v+B2l2C.dvdt
FurtherFnet=F−FmFnet=F-Fm
ormdvdt=F−B2l2Rv−B2l2Cdvdtmdvdt=F-B2l2Rv-B2l2Cdvdt
∴∫v0dvF−B2l2Rv=∫10dtm+B2l2C∴∫0vdvF-B2l2Rv=∫01dtm+B2l2C
Integrating we get,
V=FRB2l2[1−1−(B2l2mR+RB2l2C)t]V=FRB2l2[1-1-(B2l2mR+RB2l2C)t]
Terminal velocity in this case is :vT=FRB2l2

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