A rod is placed on horizontal set of frictionless rails. The rod has an effectiv

Question

A rod is placed on horizontal set of frictionless rails. The rod has an effective resistance [R] between the points of contact on the rails. The rails are connected to the poles of a battery that provides a constant potential [sigma]. A uniform magnetic field [B] is perpendicular to the plane of the rails. Write an equation for the net force acting on the rod, and then derive an expression for the terminal velocity of the rod. The battery is replaced with a charged capacitor. Write an equation for the net force acting on the rod, and then derive an expression for the terminal velocity of the rod.

Explanation / Answer

a) F = i L X B

= ibatteryLXB + iInducedLXB

= (E/R) LB - (BLv/R)LB

For terminal velocity, F = 0

BLv = E

vterminal = E/BL

b) when the battery is replaced with capacitor of Voltage V and capacitance C

F = idue to capacitorLXB + iInducedLXB

= (V e-t/RC/R) LB - (BLv/R)LB

For terminal velocity, F = 0

BLv =V e-t/RC

vterminal = V e-t/RC /BL

At large t,

vterminal = 0

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