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  • 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 Δ Φ size 12{ΔΦ} {} . Second, emf is greatest when the change in time Δ t size 12{Δt} {} is smallest—that is, emf is inversely proportional to Δ t size 12{Δt} {} . Finally, if a coil has N turns, an emf will be produced that is N size 12{N} {} times greater than for a single coil, so that emf is directly proportional to N size 12{N} {} . The equation for the emf induced by a change in magnetic flux is

emf = N Δ Φ Δ t . size 12{"emf"= - N { {ΔΦ} over {Δt} } } {}

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 Δ Φ size 12{ΔΦ} {} —this is known as Lenz’s law . The direction (given by the minus sign) of the emf is 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 [link] .)

Part a of the figure shows a bar magnet held horizontal and moved into a coil held in the same plane. The magnet is moved in such a way that the north pole of the magnet is shown to face the coil. The magnetic lines of force are shown to emerge out from the North Pole. The magnetic field associated with the bar magnet is given as B mag. The strength of the magnetic field increases in the coil. The current induced in the coil I creates another field B coil, in the opposite direction of the bar magnet to oppose the increase. So B mag and B coil are in opposite directions. In part b of the diagram, the magnet is moved away from the coil. The magnet is moved in such a way that the north pole of the magnet is shown to face the coil. The magnetic lines of force are shown to emerge out from the North Pole. The magnetic field associated with the bar magnet is given as B mag. The current induced in the coil I creates another field B coil, in the same direction as the field of the bar magnet. So B mag and B coil are in same directions. Part c of the figure shows a bar magnet held horizontal and moved into a coil held in the same plane. The magnet is moved in such a way that the south pole of the magnet is shown to face the coil. The magnetic lines of force are shown to merge into the South Pole. The magnetic field associated with the bar magnet is given as B mag. The current induced in the coil I, creates another field B coil, in the opposite direction of field of the bar magnet. So B mag and B coil are in opposite directions.
(a) When this bar magnet is thrust into the coil, the strength of the magnetic field increases in the coil. The current induced in the coil creates another field, in the opposite direction of the bar magnet’s to oppose the increase. This is one aspect of Lenz’s law—induction opposes any change in flux . (b) and (c) are two other situations. Verify for yourself that the direction of the induced B coil size 12{B rSub { size 8{"coil"} } } {} shown indeed opposes the change in flux and that the current direction shown is consistent with RHR-2.

Problem-solving strategy for lenz’s law

To use Lenz’s law to determine the directions of the induced magnetic fields, currents, and emfs:

  1. Make a sketch of the situation for use in visualizing and recording directions.
  2. Determine the direction of the magnetic field B.
  3. Determine whether the flux is increasing or decreasing.
  4. Now determine the direction of the induced magnetic field B. It opposes the change in flux by adding or subtracting from the original field.
  5. Use RHR-2 to determine the direction of the induced current I that is responsible for the induced magnetic field B.
  6. 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 [link] 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 ( [link] ). A signal in the form of a varying input current from a microphone or camera goes to the recording head. These signals (which are a function of the signal amplitude and frequency) produce varying magnetic fields at the recording head. As the tape moves past the recording head, the magnetic field orientations of the iron oxide molecules on the tape are changed thus recording the signal. In the playback mode, the magnetized tape is run past another head, similar in structure to the recording head. The different magnetic field orientations of the iron oxide molecules on the tape induces an emf in the coil of wire in the playback head. This signal then is sent to a loudspeaker or video player.

Questions & Answers

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The Critical Angle Derivation So the critical angle is defined as the angle of incidence that provides an angle of refraction of 90-degrees. Make particular note that the critical angle is an angle of incidence value. For the water-air boundary, the critical angle is 48.6-degrees.
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the ratio of the density of a substance to the density of a standard, usually water for a liquid or solid, and air for a gas.
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Practice Key Terms 2

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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