APFIVE Magnetic Force on a Sliding Rod
A conducting rod of mass m and length L slides without friction on two parallel conducting rails connected by a resistor R. A uniform magnetic field B is directed perpendicular to the plane of the rails. If the rod has an initial velocity v₀ at time t = 0, which of the following gives the magnitude of the magnetic force on the rod as a function of time t?
A
$$F = \(B^2L^2v_0/R\ e^{-\frac{B^2L^2}{mR}t}\)$$
B
$$F = (B²L²/R)e^(-Rt/L)$$
C
$$F = (B²L²/R)(1-e^(-Rt/L))$$
D
$$F = (BLv₀)e^(-B²L²t/mR)$$
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