How can I solve this?

Question

The moving rod has a resistance of 0.25Ω and moves on rails 20 cm apart. The stationary U-shaped conductor has negligible resistance. When a force of 0.350 N is applied to the rod, it moves to the right at a constant speed of 1.40 m/s. What is the magnetic field?

Answer 1

There is a lot going on in this problem! Focus on three key ideas:

1. Newton's Laws - Since the rod moves with a constant speed, the net force acting on it must be zero. That means that the force exerted on the rod by the magnetic field equals the applied force.
2. When the rod moves, the magnetic flux through the area bounded by the rod and the U-shaped conductor changes. Due to this changing magnetic flux, a voltage is induced and current flows through the rod (as well as through the U). Mathematically, I_induced = V_induced/R = BLv/R, where L is the length of the rod.
3. When current flows through the rod, the magnetic field exerts a force on the rod. The right hand rule shows that this force is opposite in direction to the applied force. The formula for this force is F = ILB.

Putting all this together, we find F = ILB = (BLv/R) L B = B²L²v/R. Solving for B, B = (FR/L²v)^1/2 = 1.25 T