Current in Loop from Falling Bar Magnet · CAP 2009 #19
Physics · electromagnetism
Problem
A bar magnet is dropped from above and falls through a loop of wire as shown. A student measures the current in the loop between a time when the north pole of the magnet is above the plane of the loop and another time when the south pole of the magnet is below the plane of the loop. Which statement is correct about the result of the student's measurement? (a) The current in the loop flows in one direction increasing steadily to its maximum value when the centre of the bar crosses the centre of the loop plane, after which the current begins to steadily decrease. (b) The current in the loop undergoes harmonic oscillations because the magnetic flux through the loop is changing. (c) The current in the loop flows first in one direction, then, after the centre of the bar crosses the centre of the loop plane, the current begins to flow in the opposite direction. (d) No current flows in the loop because both ends of the magnet move through the loop.Intuitive explanation
This problem hinges on Faraday's law and Lenz's law: the induced current depends on how the magnetic flux through the loop changes, not on which pole is closer. As the magnet falls, the flux first increases (magnet approaching), reaches a maximum as it passes through the plane, then decreases (magnet receding). Since the flux direction reverses—from north-pole-down to south-pole-down—the induced current must reverse direction to oppose these opposite changes. The key insight is tracking the sign of the flux change, not just its magnitude.
Intuitive explanation
This problem hinges on Faraday's law and Lenz's law: the induced current depends on how the magnetic flux through the loop changes, not on which pole is closer. As the magnet falls, the flux first increases (magnet approaching), reaches a maximum as it passes through the plane, then decreases (magnet receding). Since the flux direction reverses—from north-pole-down to south-pole-down—the induced current must reverse direction to oppose these opposite changes. The key insight is tracking the sign of the flux change, not just its magnitude.