Physics · Ch 6 — Electromagnetic Induction
Lenz's Law and Conservation of Energy
Lenz's Law and Conservation of Energy
Statement of Lenz's law. Faraday's law gives the magnitude of the induced emf but is silent, on its own, about which way the induced current flows. Heinrich Lenz supplied the missing rule in 1834:
The direction of an induced current is always such that it opposes the very change in magnetic flux that produced it.
This is precisely what the minus sign in encodes: the induced emf's polarity is such that any current it drives sets up its OWN magnetic flux fighting against the change in the original flux, never helping it along.
Working it out for a bar magnet and a coil. Suppose a bar magnet's NORTH pole is pushed towards a closed coil (Section 6.2's figure). The flux through the coil, due to the approaching magnet, is INCREASING. By Lenz's law, the induced current must oppose this increase, so it must create its own magnetic field pointing AWAY from the approaching magnet inside the coil -- which means the coil's near face must itself become a north pole, so as to REPEL the approaching magnet (like poles repel). Working out the current direction that makes the coil's near face a north pole (using the right-hand rule) gives the actual direction of the induced current. If the same magnet is instead WITHDRAWN, the flux is now DECREASING, so the induced current must oppose this decrease by creating a field that ATTRACTS the receding magnet -- the coil's near face must become a SOUTH pole this time, and the induced current reverses direction compared to the approaching case.
Entering and leaving a field region (the figure for this section). The same reasoning applies to a loop crossing the sharp boundary of a field region. As the loop ENTERS the field (flux into the loop increasing), the induced current flows so as to oppose the increase, creating a field that opposes the external one inside the loop; as the loop LEAVES the field (flux decreasing), the induced current reverses to oppose the decrease instead, this time reinforcing the external field inside the loop. In both cases, the magnetic force this induced current experiences from the external field acts to OPPOSE the loop's own motion -- pulling it back as it tries to enter, and pulling it back as it tries to leave. …
What this figure shows. Two separate small diagrams are drawn side by side, each showing a rectangular wire loop about to cross the sharply drawn boundary of a region containing a uniform magnetic field, shown by evenly spaced dots inside the field region (field coming OUT of the page). In the LEFT diagram, the loop is drawn just ENTERING the field region from the left, with a rightward arrow showing its direction of motion; a curved arrow is drawn on the loop itself showing the induced current flowing CLOCKWISE (as seen on the page), and a small label 'induced field into the page, opposing the increasing outward flux' sits beside the loop. In the RIGHT diagram, an identical loop is drawn just LEAVING the same field region on the right-hand side, again with a rightward arrow showing its direction of motion; the curved arrow on this loop shows the induced current flowing ANTICLOCKWISE, with a label 'induced field out of the page, opposing the decreasing outward flux'. Both diagrams include a short horizontal arrow outside the loop, labelled , pointing back towards t …