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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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Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
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Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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there is no specific books for beginners but there is book called principle of nanotechnology
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fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
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what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
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Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
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is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
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Do you know which machine is used to that process?
s.
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for screen printed electrodes ?
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of graphene you mean?
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or in general
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in general
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Graphene has a hexagonal structure
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China
Cied
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where did you find the research and the first image (ECG and Blood pressure synchronized)? Thank you!!
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Practice Key Terms 2

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Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
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