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

V = N Δ Φ Δ t .

This relationship is known as Faraday’s law of induction    .

The minus sign in Faraday’s law of induction is very important. The minus means that the induced voltage 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 . 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.

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.

Photograph of the electronic components of playback heads used with audio and video magnetic tapes.
Recording and playback heads used with audio and video magnetic tapes. (credit: Steve Jurvetson)

Similar principles apply to computer hard drives, except at a much faster rate. Here recordings are on a coated, spinning disk. Read heads historically were made to work on the principle of induction. However, the input information is carried in digital rather than analog form – a series of 0’s or 1’s are written upon the spinning hard drive. Today, most hard drive readout devices do not work on the principle of induction, but use a technique known as giant magnetoresistance . (The discovery that weak changes in a magnetic field in a thin film of iron and chromium could bring about much larger changes in electrical resistance was one of the first large successes of nanotechnology.) Another application of induction is found on the magnetic stripe on the back of your personal credit card as used at the grocery store or the ATM machine. This works on the same principle as the audio or video tape mentioned in the last paragraph in which a head reads personal information from your card.

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Source:  OpenStax, Concepts of physics. OpenStax CNX. Aug 25, 2015 Download for free at https://legacy.cnx.org/content/col11738/1.5
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