Motional emf: A conducting bar slides without friction on two parallel horizontal rails that are 50 cm apart and connected by a wire at one end. The resistance of the bar and the rails is constant and equal to 0.10 Ω. A uniform magnetic field is perpendicular to the plane of the rails. A 0.080-N force parallel to the rails is required to keep the bar moving at a constant speed of 0.50 m/s. What is the magnitude of the magnetic field?
A) 0.10 T
B) 0.25 T
C) 0.36 T
D) 0.54 T
E) 0.93 T

Question

Quizplus · Accepted Answer

The force required to keep the bar moving 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 current I can be found using Ohm's law, I = V/R, where V is the motional emf, V = BLv. Substituting these into the force equation and solving for B gives B = F/(LvR) = 0.080 N / (0.50 m/s * 0.50 m * 0.10 Ω) = 0.25 T.

Motional Emf: a Conducting Bar Slides Without Friction on Two