Faraday's law of induction

From Wikipedia, the free encyclopedia

Image:Solenoid.svg
Electromagnetism
Electricity · Magnetism
Electrostatics Electric charge Coulomb's law Electric field Gauss's law Electric potential Electric dipole moment
Magnetostatics Ampère's circuital law Magnetic field Magnetic flux Biot-Savart law Magnetic dipole moment
Electrodynamics Electric current Lorentz force law Electromotive force Electromagnetic induction Faraday's law of induction Displacement current Maxwell's equations Electromagnetic field Electromagnetic radiation
Electrical Network Conduction Resistance Capacitance Inductance Impedance Resonant cavities Waveguides
Tensors in Relativity Electromagnetic tensor Electromagnetic stress-energy    tensor
This box: view • talk • edit

Faraday's law of induction (or the law of electromagnetic induction) states that the induced electromotive force in a closed loop is directly proportional to the time rate of change of magnetic flux through the loop.

Moving a conductor (such as a metal wire) through a magnetic field produces a voltage in that conductor. The resulting voltage is proportional to the speed of movement: moving the conductor twice as fast produces twice the voltage. The magnetic field, the direction of movement, and the voltage are all at right angles to each other. Whenever movement creates voltage, Fleming's right hand rule describes the direction of the voltage. A fixed conductor will also have an induced voltage if the magnetic flux in the area enclosed by the conductor is changing.

For the common but special case of a coil of wire, composed of N loops with the same area, Faraday's law of electromagnetic induction states that

<math> \mathcal{E} = - N{{d\Phi_B} \over dt}</math>

where

<math>\mathcal{E}</math> is the electromotive force (emf) in volts

N is the number of turns of wire

Φ_B is the magnetic flux in webers through a single loop. The direction of the electromotive force (the negative sign in the above formula) was first given by Lenz's law.

More generally, the relation between the rate of change of the magnetic flux through the surface S enclosed by a contour C and the electric field along the contour is defined as:

<math>\oint_C \mathbf{E} \cdot d\mathbf{l} = - \ { d \over dt } \int_S \mathbf{B} \cdot d\mathbf{A}</math>

where

E is the electric field,

dl is an infinitesimal element of the contour C,

B is the magnetic field.

The directions of the contour C and of <math>d\mathbf{A}</math> are assumed to be related by the right-hand rule.

Equivalently, the differential form of Faraday's law is

<math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>

which is one of the Maxwell equations.

This principle is used for measuring the flow of electrically conductive liquids and slurries. Such instruments are called Magnetic Flow Meters. The induced voltage U generated in the magnetic field B due to a conductive liquid moving at velocity v is thus given by:

<math>\mathbf U= BLv</math>,

where L is the distance between electrodes in the magnetic flow meter.

Faraday's law, along with the other laws of electromagnetism, was later incorporated into Maxwell's equations, unifying all of electromagnetism.

Faraday's law of induction is based on Michael Faraday's experiments in 1831. The effect was also discovered by Joseph Henry at about the same time, but Faraday published first.^[1][2]

Lenz's law gives the direction of the induced electromotive force (emf) and current resulting from electromagnetic induction. German physicist Heinrich Lenz formulated it in 1834

Contents 1 Practical Demonstration 2 Applications 3 See also 4 References

[edit] Practical Demonstration

A brief but informative video demonstrating Faraday's Law may be watched at EduMation.

[edit] Applications

The principles of electromagnetic induction are applied in many devices and systems, including:

[edit] See also

• Magnetic field
• Magnetic flux
• Michael Faraday
• Ampère's law
• Lenz's law
• Lorentz force
• Stokes' theorem
• Vector calculus
• Moving magnet and conductor problem
• Crosstalk, an electrical interference caused by this law.

[edit] References

1. ^ Ulaby, Fawwaz (2001-01-31). Fundamentals of Applied Electromagnetics, 2nd edition, Prentice Hall, p. 232. ISBN 0-13-032931-2. 
2. ^ Joseph Henry. Distinguished Members Gallery, National Academy of Sciences. Retrieved on 2006-11-30.

af:Faraday se wet

ar:قانون فاراداي-لينز bn:ফ্যারাডের আবেশ সূত্র ca:Llei de Faraday cs:Zákon elektromagnetické indukce de:Elektromagnetische Induktion#Induktionsgesetz es:Ley de Faraday fr:Loi de Faraday it:Legge di Faraday-Neumann-Lenz he:חוק פאראדיי hr:Elektromagnetska indukcija ms:Hukum aruhan Faraday nl:Inductiewet van Faraday ja:ファラデーの電磁誘導の法則 no:Faradays lov pl:Prawo indukcji elektromagnetycznej Faradaya pt:Lei de Faraday-Neumann-Lenz sl:Indukcijski zakon sr:Фарадејев закон електромагнетне индукције fi:Faradayn induktiolaki vi:Định luật cảm ứng Faraday zh:法拉第电磁感应定律