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Electromagnetic Radiation
In physics , ELECTROMAGNETIC RADIATION (EM RADIATION or EMR) refers to the waves (or their quanta, photons ) of the electromagnetic field , propagating (radiating) through space carrying electromagnetic radiant energy . It includes radio waves , microwaves , infrared , (visible) light , ultraviolet , X- , and gamma radiation. Classically , electromagnetic radiation consists of ELECTROMAGNETIC WAVES, which are synchronized oscillations of electric and magnetic fields that propagate at the speed of light through a vacuum . The oscillations of the two fields are perpendicular to each other and perpendicular to the direction of energy and wave propagation, forming a transverse wave . The wavefront of electromagnetic waves emitted from a point source (such as a lightbulb) is a sphere . The position of an electromagnetic wave within the electromagnetic spectrum could be characterized by either its frequency of oscillation or its wavelength
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Mathematical Descriptions Of The Electromagnetic Field
MATHEMATICS (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of topics such as quantity (numbers), structure , space , and change . There are many views among mathematicians and philosophers as to the exact scope and definition of mathematics . Mathematicians seek out patterns and use them to formulate new conjectures . Mathematicians resolve the truth or falsity of conjectures by mathematical proof . When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic , mathematics developed from counting , calculation , measurement , and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry
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Electrical Network
An ELECTRICAL NETWORK is an interconnection of electrical components (e.g. batteries , resistors , inductors , capacitors , switches ) or a model of such an interconnection, consisting of electrical elements (e.g. voltage sources , current sources , resistances , inductances , capacitances ). An ELECTRICAL CIRCUIT is a network consisting of a closed loop, giving a return path for the current. Linear electrical networks, a special type consisting only of sources (voltage or current), linear lumped elements (resistors, capacitors, inductors), and linear distributed elements (transmission lines), have the property that signals are linearly superimposable . They are thus more easily analyzed, using powerful frequency domain methods such as Laplace transforms , to determine DC response , AC response , and transient response . A RESISTIVE CIRCUIT is a circuit containing only resistors and ideal current and voltage sources
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Transverse Wave
A TRANSVERSE WAVE is a moving wave that consists of oscillations occurring perpendicular (right angled) to the direction of energy transfer (or the propagation of the wave). If a transverse wave is moving in the positive x-direction, its oscillations are in up and down directions that lie in the y–z plane. Light
Light
is an example of a transverse wave, while sound is a longitudinal wave . A ripple in a pond and a wave on a string are easily visualized as transverse waves. CONTENTS* 1 Explanation * 1.1 "Polarized" waves * 1.2 Electromagnetic waves * 2 See also * 3 References * 4 External links EXPLANATIONTransverse waves are waves that are oscillating perpendicularly to the direction of propagation. If you anchor one end of a ribbon or string and hold the other end in your hand, you can create transverse waves by moving your hand up and down. Notice though, that you can also launch waves by moving your hand side-to-side
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Magnetic Potential
The term MAGNETIC POTENTIAL can be used for either of two quantities in classical electromagnetism : the magnetic vector potential, A, (often simply called the vector potential) and the magnetic scalar potential, ψ. Both quantities can be used in certain circumstances to calculate the magnetic field . The more frequently used magnetic vector potential, A, is defined such that the curl of A is the magnetic field B. Together with the electric potential , the magnetic vector potential can be used to specify the electric field , E as well. Therefore, many equations of electromagnetism can be written either in terms of the E and B, or in terms of the magnetic vector potential and electric potential. In more advanced theories such as quantum mechanics , most equations use the potentials and not the E and B fields
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Lenz's Law
LENZ\'S LAW (pronounced /ˈlɛnts/ ), named after the physicist Emil Lenz who formulated it in 1834, says: The direction of current induced in a conductor by a changing magnetic field due to Faraday\'s law of induction will be such that it will create a magnetic field that opposes the change that produced it. Lenz's law
Lenz's law
is shown by the negative sign in Faraday\'s law of induction : E = t , {displaystyle {mathcal {E}}=-{frac {partial Phi }{partial t}},} which indicates that the induced EMF ( E {displaystyle {mathcal {E}}} ) and the change in magnetic flux ( {displaystyle partial Phi } ) have opposite signs. It is a qualitative law that specifies the direction of induced current but says nothing about its magnitude
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Displacement Current
In electromagnetism , DISPLACEMENT CURRENT is a quantity appearing in Maxwell\'s equations that is defined in terms of the rate of change of electric displacement field . Displacement current
Displacement current
has the same units as electric current, and it is a source of the magnetic field just as actual current is. However it is not an electric current of moving charges , but a time-varying electric field . In physical materials (as opposed to vacuum), there is also a contribution from the slight motion of charges bound in atoms, called dielectric polarization . The idea was conceived by James Clerk Maxwell
James Clerk Maxwell
in his 1861 paper On Physical Lines of Force, Part III in connection with the displacement of electric particles in a dielectric medium. Maxwell added displacement current to the electric current term in Ampère\'s Circuital Law
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Electromagnetic Induction
ELECTROMAGNETIC or MAGNETIC INDUCTION is the production of an electromotive force (i.e., voltage) across an electrical conductor due to its dynamic interaction with a magnetic field . Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell
James Clerk Maxwell
mathematically described it as Faraday\'s law of induction . Lenz\'s law describes the direction of the induced field. Faraday's law was later generalized to become the Maxwell-Faraday equation, one of the four Maxwell\'s equations in James Clerk Maxwell's theory of electromagnetism. Electromagnetic induction
Electromagnetic induction
has found many applications in technology, including electrical components such as inductors and transformers , and devices such as electric motors and generators
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Biot–Savart Law
In physics , specifically electromagnetism , the BIOT–SAVART LAW (/ˈbiːoʊ səˈvɑːr/ or /ˈbjoʊ səˈvɑːr/ ) is an equation describing the magnetic field generated by an electric current . It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The law is valid in the magnetostatic approximation , and is consistent with both Ampère\'s circuital law and Gauss\'s law for magnetism . It is named after Jean-Baptiste Biot
Jean-Baptiste Biot
and Félix Savart who discovered this relationship in 1820
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Gauss's Law For Magnetism
In physics , GAUSS\'S LAW FOR MAGNETISM is one of the four Maxwell\'s equations that underlie classical electrodynamics . It states that the magnetic field B has divergence equal to zero, in other words, that it is a solenoidal vector field . It is equivalent to the statement that magnetic monopoles do not exist. Rather than "magnetic charges", the basic entity for magnetism is the magnetic dipole . (Of course, if monopoles were ever found, the law would have to be modified, as elaborated below.) Gauss's law for magnetism can be written in two forms, a differential form and an integral form. These forms are equivalent due to the divergence theorem . The name " Gauss's law for magnetism" is not universally used. The law is also called "Absence of free magnetic poles "; one reference even explicitly says the law has "no name"
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Lorentz Force
In physics (particularly in electromagnetism ) the LORENTZ FORCE is the combination of electric and magnetic force on a point charge due to electromagnetic fields . A particle of charge q moving with velocity V in the presence of an electric field E and a magnetic field B experiences a force F = q E + q v B {displaystyle mathbf {F} =qmathbf {E} +qmathbf {v} times mathbf {B} } (in SI units ). Variations on this basic formula describe the magnetic force on a current-carrying wire (sometimes called Laplace force), the electromotive force in a wire loop moving through a magnetic field (an aspect of Faraday\'s law of induction ), and the force on a charged particle which might be travelling near the speed of light (relativistic form of the Lorentz force)
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Maxwell Stress Tensor
The MAXWELL STRESS TENSOR (named after James Clerk Maxwell
James Clerk Maxwell
) is a second-order tensor used in classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum . In simple situations, such as a point charge moving freely in a homogeneous magnetic field, it is easy to calculate the forces on the charge from the Lorentz force
Lorentz force
law . When the situation becomes more complicated, this ordinary procedure can become impossibly difficult, with equations spanning multiple lines. It is therefore convenient to collect many of these terms in the Maxwell stress tensor, and to use tensor arithmetic to find the answer to the problem at hand. In the relativistic formulation of electromagnetism, the Maxwell's tensor appears as a part of the electromagnetic stress–energy tensor which is the electromagnetic component of the total stress–energy tensor
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Faraday's Law Of Induction
FARADAY\'S LAW OF INDUCTION is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF) —a phenomenon called electromagnetic induction . It is the fundamental operating principle of transformers , inductors , and many types of electrical motors , generators and solenoids . The MAXWELL–FARADAY EQUATION is a generalization of Faraday's law, and is listed as one of Maxwell\'s equations . CONTENTS * 1 History * 2 Faraday\'s law * 2.1 Qualitative statement * 2.2 Quantitative * 2.3 Maxwell–Faraday equation * 3 Proof of Faraday\'s law * 4 EMF for non-thin-wire circuits * 5 Faraday\'s law and relativity * 5.1 Two phenomena * 5.2 Einstein\'s view * 6 See also * 7 References * 8 Further reading * 9 External links HISTORY A diagram of Faraday's iron ring apparatus
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Eddy Current
EDDY CURRENTS (also called FOUCAULT CURRENTS ) are loops of electrical current induced within conductors by a changing magnetic field in the conductor, due to Faraday\'s law of induction . Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. They can be induced within nearby stationary conductors by a time-varying magnetic field created by an AC electromagnet or transformer , for example, or by relative motion between a magnet and a nearby conductor. The magnitude of the current in a given loop is proportional to the strength of the magnetic field, the area of the loop, and the rate of change of flux, and inversely proportional to the resistivity of the material. By Lenz\'s law , an eddy current creates a magnetic field that opposes a change in the magnetic field that created it, and thus eddy currents react back on the source of the magnetic field
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Electrical Resistance And Conductance
The ELECTRICAL RESISTANCE of an electrical conductor is a measure of the difficulty to pass an electric current through that conductor. The inverse quantity is ELECTRICAL CONDUCTANCE, and is the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with the notion of mechanical friction . The SI unit of electrical resistance is the ohm (Ω ), while electrical conductance is measured in siemens (S). An object of uniform cross section has a resistance proportional to its resistivity and length and inversely proportional to its cross-sectional area. All materials show some resistance, except for superconductors , which have a resistance of zero
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Ohm's Law
OHM\'S LAW states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance , one arrives at the usual mathematical equation that describes this relationship: I = V R , {displaystyle I={frac {V}{R}},} where I is the current through the conductor in units of amperes , V is the voltage measured across the conductor in units of volts , and R is the resistance of the conductor in units of ohms . More specifically, Ohm's law
Ohm's law
states that the R in this relation is constant, independent of the current. The law was named after the German physicist Georg Ohm
Ohm
, who, in a treatise published in 1827, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire
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