ELECTROMAGNETISM & RELATIVITY - Chapter 5, Exercise 2 Solution ========================================================== Conceptual: Lenz's Law and a Magnet Approaching a Coil PROBLEM ------- A bar magnet's north pole is pushed toward a coil of wire, increasing the magnetic flux through the coil. Using Lenz's law, explain (in terms of opposing the change) what direction the induced current must flow, and why - without needing to specify a literal clockwise/counterclockwise answer. SOLUTION -------- As the magnet's north pole approaches the coil, the magnetic flux passing through the coil (from the magnet's own field) is increasing. By Lenz's law, the induced current in the coil must flow in whatever direction creates its OWN magnetic field that OPPOSES this increase. Since the approaching field is growing stronger in one particular direction through the coil, the induced current must generate a magnetic field of its own pointing in the OPPOSITE direction through the coil - partially cancelling, not reinforcing, the magnet's own growing field. A useful physical way to think about this: the induced current's own magnetic field must effectively make the coil's near face act like a north pole too, facing the approaching magnet's own north pole. Since like poles repel, this means the coil genuinely pushes back against the approaching magnet - the induced current creates a real, physical resistance to the magnet being pushed closer. ANSWER: The induced current flows in whatever direction makes the coil's near face effectively become a north pole, repelling the approaching magnet's own north pole - directly opposing the increasing flux (and the magnet's own approach) exactly as Lenz's law requires, rather than assisting it. ---- WHY THIS WORKS AS AN ANSWER This connects Lenz's law directly to the chapter's own deeper explanation: if the induced current instead created a field that REINFORCED the magnet's approach (attracting it further in rather than repelling it), the magnet would accelerate toward the coil with no outside force required, releasing energy from nothing - a direct violation of conservation of energy. The repulsive, opposing behavior demonstrated here is not an arbitrary rule; it is required for energy to be conserved, since work must be done (by whoever or whatever is pushing the magnet) to overcome this induced opposition and actually make the magnet approach the coil.