The drawing shows three identical rods (A, B, and C) moving in different planes.

Question

The drawing shows three identical rods (A, B, and C) moving in different planes. A constant magnetic field of magnitude 3.50 T is directed along the + y axis. The length of each rod is L = 1.3 m, and the rods each have the same speed, v_A = v_B = v_C = 3.2 m/s. For each rod, find the magnitude of the motional emf, and indicate which end (1 or 2) of the rod is positive. rod A ____ V rod B ____ V rod C _____ V Suppose that the voltage of the battery in the circuit is 2.7 V, the magnitude of the magnetic field (directed perpendicularly into the plane of the screen) is 0.64 T, and the length of the rod between the rails is 0.19 m. Assuming that the rails are very long and have negligible resistance, find the maximum speed attained by the rod after the switch is closed. _____ m/s Suppose that the light bulb in the figure is a 58.8-W bulb with a resistance of 220 Ohm. The magnetic field has a magnitude of 0.41 T, and the length of the rod is 0.67 m. The only resistance in the circuit is that due to the bulb. What is the shortest distance along the rails that the rod would have to slide for the bulb to remain lit for one-half second? ____ m

Explanation / Answer

1. motional emf on a rod moving with velocity v in external magnetic field B is given by, V = Blv
given, L = 1.3m
B = 3.5 T j [ j is unit vector along y axis ]
v = 3.2 m/s
so, for conductor with velocity, motional emf = 0 [ as the direction of velocity is not perpendicular to that of magnetic field]
similiarly, the rod with speed va has 0 mtioonal EMF
motional emf on the rod with speed Vb = Blv = 3.5*1.3*3.2 = 14.56 V, end 2 is +ve
2. V = 2.7 V
B = 0.64 T
length of rods between rails, l = 0.19 m
so, when the maximum speed is attained then net force on the rod s zero
magnetic force = Bil [ i is net current from the rod]
now V = Blv
v = V/Bl = 22.2039 m/s

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