Question

A rod moves along two horizontal frictionless conducting rails. A uniform constant magnetic field is perpendicular to the plane of the rails. If a constant force moves the bar at a constant velocity, what is the current?

Answer 1

A rod moving in a magnetic field perpendicular to it induces an emf which can be calculated with ε = Bvl. The current is then I = ε/R, found by dividing the emf by the total circuit resistance.

Step-by-step explanation:

When a conducting rod moves along two horizontal frictionless conducting rails within a uniform magnetic field that is perpendicular to the plane of the rails, an electromotive force (emf) is induced in the rod due to the change in magnetic flux through the circuit. If the rod moves at a constant velocity, the emf (ε) induced can be calculated using the formula ε = Bvl, where B is the magnetic field strength, v is the velocity of the rod, and l is the length of the rod between the rails. Knowing the emf and the total resistance R of the circuit (including the rod, rails, and any external resistance), the current I can then be calculated using Ohm’s law, I = ε/R.

For example, if a rod is moving with a speed of 5.0 m/s in a magnetic field of 0.25 T, and the distance between the rails is 25 cm with a resistance of 2.0 Ω, then the induced emf is ε = Bvl = 0.25 T * 5.0 m/s * 0.25 m = 0.3125 V. The current induced can be calculated as I = ε/R = 0.3125 V / 2.0 Ω = 0.15625 A.