A conducting bar slides without friction on two parallel horizontal rails 50 cm apart. The resistance of the bar and the rails is assumed to be constant and equal to 0.1 Ω. A uniform magnetic field is perpendicular to the plane of the rails. A force F = 0.08 N is required to keep the bar moving at a constant speed of 0.5 m/s. What is the magnitude of the magnetic field?

Question

Quizplus · Accepted Answer

The force required to keep the bar moving at a constant speed is equal to the magnetic force, which is given by F = BIL, where B is the magnetic field, I is the current, and L is the length of the bar. The induced emf (ε) is given by ε = BLv, where v is the velocity. The current I can be found using Ohm's law: I = ε/R = BLv/R. Substituting I in the force equation gives F = B(BLv/R)L = B^2L^2v/R. Solving for B gives B = sqrt(FR/(L^2v)). Substituting the given values, B = sqrt(0.08 * 0.1 / (0.5^2 * 0.5)) = 0.25 T.

A Conducting Bar Slides Without Friction on Two Parallel Horizontal