Question

A conducting rod of length I, mass m and resistance R is falling freely through a uniform magnetic field B which is perpendicular to the plane of paper as shown in figure Find terminal velocity (vt) of this rod. [Ans :mgR/B²l²]

Answer 1

The emf driving the current is equivalent to vBd where d is the length of the segment of wire interfacing the rails.

(The work done per unit charge (voltage) is vBd, when a charge moves from one end of the moving wire to the opposite end.)

The present streaming in the circuit will be I = vBd/R,

where R is the obstruction of the circuit.

Subsequently v = IR/Bd = 0.5 A*6 Ω/(2.5 T*1.2 m) = 1 m/s.