Problem 34.39 (RHK)
As shown in the figure, a metal strip, 6.5 cm long, 0.88 cm wide, and 0.76 cm thick, moves with constant velocity through a magnetic field perpendicular to the strip. A potential difference of is measured between points x and y across the strip. We have to calculate the speed v.
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Let n be the volume density of conduction charge carriers inside the metal strip. As the strip is being pulled with velocity , the charge carriers also move with velocity in the laboratory frame in which the magnetic field is static and uniform. The Hall electric field, E, is related to the potential difference, V, measured across the strip and the width of the strip, w.
Also, when the Hall voltage becomes constant, the net Lorentz force on the conduction charge carriers will be zero. That is
From the data of the problem, we note that
Therefore, the speed v with which the strip is being pulled is