30.4 Lenz’s Law
We started out by looking at a situation in which a moving wire caused a loop to expand in a magnetic field. This is one way to change the magnetic flux through the loop. But Faraday found that a current can be induced by any change in the magnetic flux, no matter how it’s accomplished.
For example, a momentary current is induced in the loop of FIGURE 30.18 as the bar magnet is pushed toward the loop, increasing the flux through the loop. Pulling the magnet back out of the loop causes the current meter to deflect in the opposite direction. The conducting wires aren’t moving, so this is not a motional emf. Nonetheless, the induced current is very real.
FIGURE 30.18 Pushing a bar magnet toward the loop induces a current.
The German physicist Heinrich Lenz began to study electromagnetic induction after learning of Faraday’s discovery. Three years later, in 1834, Lenz announced a rule for determining the direction of the induced current. We now call his rule Lenz’s law, and it can be stated as follows:
Lenz’s law is rather subtle, and it takes some practice to see how to apply it.
NOTE One difficulty with Lenz’s law is the term “flux.” In everyday language, the word “flux” already implies that something is changing. Think of the phrase, “The situation is in flux.” Not so in physics, where “flux,” the root of the word “flow,” means “passes through.” A steady magnetic field through a loop creates a steady, unchanging magnetic flux.
Lenz’s law tells us to look for situations where the flux is changing. This can happen in three ways.
The magnetic field through the loop changes (increases or decreases),
The loop changes in area or angle, or
The loop moves into or out of a magnetic field.
Lenz’s law depends on the idea that an induced current generates its own magnetic field . This is the induced magnetic field of Lenz’s law. You learned in Chapter 29 how to use the right-hand rule to determine the direction of this induced magnetic field.
In Figure 30.18, pushing the bar magnet toward the loop causes the magnetic flux to increase in the downward direction. To oppose the change in flux, which is what Lenz’s law requires, the loop itself needs to generate the upward-pointing magnetic field of FIGURE 30.19. The induced magnetic field at the center of the loop will point upward if the current is ccw. Thus pushing the north end of a bar magnet toward the loop induces a ccw current around the loop. The induced current ceases as soon as the magnet stops moving.
FIGURE 30.19 The induced current is ccw.
Now suppose the bar magnet is pulled back away from the loop, as shown in FIGURE 30.20a. There is a downward magnetic flux through the loop, but the flux decreases as the magnet moves away. According to Lenz’s law, the induced magnetic field of the loop opposes this decrease. To do so, the induced field needs to point in the downward direction, as shown in FIGURE 30.20b. Thus as the magnet is withdrawn, the induced current is clockwise (cw), opposite to the induced current of Figure 30.19.
FIGURE 30.20 Pulling the magnet away induces a cw current.
NOTE Notice that the magnetic field of the bar magnet is pointing downward in both Figures 30.19 and 30.20. It is not the flux due to the magnet that the induced current opposes, but the change in the flux. This is a subtle but critical distinction. If the induced current opposed the flux itself, the current in both Figures 30.19 and 30.20 would be ccw to generate an upward magnetic field. But that’s not what happens. When the field of the magnet points down and is increasing, the induced current opposes the increase by generating an upward field. When the field of the magnet points down but is decreasing, the induced current opposes the decrease by generating a downward field.