Electromagnetic Induction, AC Circuits, and Electrical Technologies
Electromagnetic Induction, AC Circuits, and Electrical Technologies
47 Faraday’s Law of Induction: Lenz’s Law
Learning Objectives
- Calculate emf, current, and magnetic fields using Faraday’s Law.
- Explain the physical results of Lenz’s Law
Faraday’s and Lenz’s Law
Faraday’s experiments showed that the emf induced by a change in magnetic flux depends on only a few factors. First, emf is directly proportional to the change in flux [latex]\Delta \Phi[/latex]. Second, emf is greatest when the change in time [latex]\Delta t[/latex] is smallest—that is, emf is inversely proportional to [latex]\Delta t[/latex]. Finally, if a coil has [latex]N[/latex] turns, an emf will be produced that is [latex]N[/latex] times greater than for a single coil, so that emf is directly proportional to [latex]N[/latex]. The equation for the emf induced by a change in magnetic flux is
This relationship is known as Faraday’s law of induction. The units for emf are volts, as is usual.
The minus sign in Faraday’s law of induction is very important. The minus means that the emf creates a current I and magnetic field B that oppose the change in flux [latex]\Delta \Phi[/latex]—this is known as Lenz’s law. The direction (given by the minus sign) of the emfis so important that it is called Lenz’s law after the Russian Heinrich Lenz (1804–1865), who, like Faraday and Henry,independently investigated aspects of induction. Faraday was aware of the direction, but Lenz stated it so clearly that he is credited for its discovery. (See Figure 47.1.)
Problem-Solving Strategy for Lenz’s Law
To use Lenz’s law to determine the directions of the induced magnetic fields, currents, and emfs:
- Make a sketch of the situation for use in visualizing and recording directions.
- Determine the direction of the magnetic field B.
- Determine whether the flux is increasing or decreasing.
- Now determine the direction of the induced magnetic field B. It opposes the change in flux by adding or subtracting from the original field.
- Use RHR-2 to determine the direction of the induced current I that is responsible for the induced magnetic field B.
- The direction (or polarity) of the induced emf will now drive a current in this direction and can be represented as current emerging from the positive terminal of the emf and returning to its negative terminal.
For practice, apply these steps to the situations shown in Figure 47.1 and to others that are part of the following text material.
Applications of Electromagnetic Induction
There are many applications of Faraday’s Law of induction, as we will explore in this chapter and others. At this juncture, let us mention several that have to do with data storage and magnetic fields. A very important application has to do with audio and video recording tapes. A plastic tape, coated with iron oxide, moves past a recording head. This recording head is basically a round iron ring about which is wrapped a coil of wire—an electromagnet (Figure 47.2). A signal in the form o