A 0.2kg metal rod carrying a current of 10.0A glides on two horizonal rails 0.500m apart. What vertical magnetic field is required to keep the rod moving at a constant speed if the coefficient of kinetic friction between the rod and rails is 0.100?
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Suppose the magnetic field is B (which is a vector and in SI unit), then the force on the rod (due to the magnetic fields) is
F = I*l x B, I is the current, and l is the length (vector).
(for more details, check the Biot-Savart Law)
If the coefficient of kinetic friction between the rod and rail is 0.1, the kinetic friction f would be
f = (Normal force)*(0.1) = (0.2)(g)(0.1), suppose g = 10, f =0.2.
Since the rod moves at constant speed, F = f,
0.2 = f = F = IlB = 10*0.05*B, B = 0.2/(10*0.05) = 0.4 (Tesla)