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Learning objectives

By the end of this section, you will be able to:

  • 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

preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Manuel Reply
Because HE needs someone to dominate the earth (Gen. 1:26)
Olorunfemi
Is the object in a conductor or an insulator? Justify your answer. whats the answer to this question? pls need help figure is given above
Jun Reply
how do i calculate the pressure on the base of a deposit if the deposit is moving with a linear aceleration
ximena Reply
why electromagnetic induction is not used in room heater ?
Gopi Reply
What is position?
Amoah Reply
What is law of gravition
sushil Reply
what is magnetism
Sandeep Reply
what is charging by induction
Sandeep Reply
what is electric field lines
Sandeep Reply
law of gravitation
Rakesh Reply
Suppose a 0.250-kg ball is thrown at 15.0 m/s to a motionless person standing on ice who catches it with an outstretched arm as shown in [link] . (b) What is his angular velocity if each arm is 5.00 kg? You may treat the ball as a point mass and treat the person's arms as uniform rods (each has a length of 0.900 m) and the rest of his body as a uniform cylinder of radius 0.180 m. Neglect the effect of the ball on his center of mass so that his center of mass remains in his geometrical center.
Varun Reply
Practice Key Terms 2

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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