10.2 Lenz’s Law
LEARNING OBJECTIVES
- Use Lenz’s law to determine the direction of induced emf whenever a magnetic flux changes
- Use Faraday’s law with Lenz’s law to determine the induced emf in a coil and in a solenoid
The direction in which the induced emf drives current around a wire loop can be found through the negative sign. However, it is usually easier to determine this direction with Lenz’s law, named in honor of its discoverer, Heinrich Lenz (1804–1865). (Faraday also discovered this law, independently of Lenz.) We state Lenz’s law as follows:
LENZ’S LAW
The direction of the induced emf drives current around a wire loop to always oppose the change in magnetic flux that causes the emf.
Lenz’s law can also be considered in terms of conservation of energy. If pushing a magnet into a coil causes current, the energy in that current must have come from somewhere. If the induced current causes a magnetic field opposing the increase in field of the magnet we pushed in, then the situation is clear. We pushed a magnet against a field and did work on the system, and that showed up as current. If it were not the case that the induced field opposes the change in the flux, the magnet would be pulled in produce a current without anything having done work. Electric potential energy would have been created, violating the conservation of energy.
To determine an induced emf , you first calculate the magnetic flux and then obtain . The magnitude of is given by . Finally, you can apply Lenz’s law to determine the sense of . This will be developed through examples that illustrate the following problem-solving strategy.
Problem-Solving Strategy: Lenz’s Law
To use Lenz’s law to determine the directions of induced magnetic fields, currents, and emfs:
- Make a sketch of the situation for use in visualizing and recording directions.
- Determine the direction of the applied magnetic field .
- Determine whether its magnetic flux is increasing or decreasing.
- Now determine the direction of the induced magnetic field . The induced magnetic field tries to reinforce a magnetic flux that is decreasing or opposes a magnetic flux that is increasing. Therefore, the induced magnetic field adds or subtracts to the applied magnetic field, depending on the change in magnetic flux.
- Use right-hand rule 2 (RHR-2; see Magnetic Forces and Fields) to determine the direction of the induced current that is responsible for the induced magnetic field .
- The direction (or polarity) of the induced emf can now drive a conventional current in this direction.
Let’s apply Lenz’s law to the system of Figure 10.2.1(a). We designate the “front” of the closed conducting loop as the region containing the approaching bar magnet, and the “back” of the loop as the other region. As the north pole of the magnet moves toward the loop, the flux through the loop due to the field of the magnet increases because the strength of field lines directed from the front to the back of the loop is increasing.