What is the magnetic field?

Question

A moving rod has a resistance of 0.25 ΩΩ and moves on rails 20.0 cm apart. The stationary U-shaped conductor has negligible resistance. When a force of 0.490 N is applied to the rod, it moves to the right at a constant speed of 1.70 m/s.

Answer 1

The key to this problem is that the acceleration of the rod is zero which means that the net force on it is zero.

There are two forces on the rod, the externally applied .49 N and the force on the current carrying rod due to the magnetic field. These must be equal and opposite.

The formula for the force on a current carrying rod is F = L B i where i is the current, L is the length of the rod and B is the magnetic field. Thus .49 = (.2) B i. So if the current can be found, B is determined.

The current is given by i = enf / R = emf / .25, where emf is the induced Faraday emf given by

emf = B v L = B 1.7 (.2) . So i = B 1.7 (.2) / .25. The force is then

F = (.2) B B 1.7 (.2) / .25 = .49

Solving for B gives B = 1.34 Tesla