Physics
Physics
Problem
A conducting rod of length slides to the right at constant speed on frictionless rails that complete a rectangular circuit with a resistor. The region contains a uniform magnetic field directed into the page. While the rod moves at constant speed, which statement best describes the horizontal force that must be applied to the rod? a) A constant force directed to the left is required to counteract the induced current in the rod. b) A force whose magnitude is proportional to the square of the rod’s speed, , must be applied to the right. c) A constant force directed to the right and equal in magnitude to the magnetic force on the rod is required. d) No external force is required once the rod is moving, because magnetic forces act only on stationary charges.Intuitive explanation
The key insight is recognizing the energy balance in this system: as the rod moves through the magnetic field, it generates an induced EMF that drives a current through the resistor, and that current-carrying rod experiences a magnetic force opposing its motion. To maintain constant speed, an external force must exactly balance this magnetic braking force—not overcome it, just match it. This is why the applied force equals the magnetic force, not exceeds it.
Intuitive explanation
The key insight is recognizing the energy balance in this system: as the rod moves through the magnetic field, it generates an induced EMF that drives a current through the resistor, and that current-carrying rod experiences a magnetic force opposing its motion. To maintain constant speed, an external force must exactly balance this magnetic braking force—not overcome it, just match it. This is why the applied force equals the magnetic force, not exceeds it.