Information about Classical Electromagnetism
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Classical electromagnetism (or classical electrodynamics) is a theory of electromagnetism that was developed over the course of the 19th century, most prominently by James Clerk Maxwell. It provides an excellent description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible (see quantum electrodynamics).
Mathematically it follows from applying the Lorentz transformation to the Coulomb force of a point electric charge to find the force between moving charges.
Lorentz force
The electromagnetic field exerts the following force (often called the Lorentz force) on charged particles:
where all boldfaced quantities are vectors: F is the force that a charge q experiences, E is the electric field at q's location, v is q's velocity, B is the strength of the magnetic field at q's position.
This description of the force between charged particles, unlike Coulomb's force law, does not break down under relativity and in fact, the magnetic force is seen as part of the relativistic interaction of fast-moving charges that Coulomb's law neglects.
The electric field E
The electric field E is defined such that, on a stationary charge:
where q0 is what is known as a test charge. The size of the charge doesn't really matter, as long as it is small enough as to not influence the electric field by its mere presence. What is plain from this definition, though, is that the unit of E is N/C, or newtons per coulomb. This unit is equal to V/m (volts per meter), see below.
The above definition seems a little bit circular but, in electrostatics, where charges are not moving, Coulomb's law works fine. So what we end up with is:
where n is the number of charges, qi is the amount of charge associated with the 'i'th charge, ri is the position of the 'i'th charge, r is the position where the electric field is being determined, and ε0 is a universal constant called the permittivity of free space.
Note: the above is just Coulomb's law, divided by q1, adding up multiple charges.
Changing the summation to an integral yields the following:
where ρ is the charge density as a function of position, runit is the unit vector pointing from dV to the point in space E is being calculated at, and r is the distance from the point E is being calculated at to the point charge.
Both of the above equations are cumbersome, especially if one wants to calculate E as a function of position. There is, however, a scalar function called the electrical potential that can help. Electric potential, also called voltage (the units for which are the volt), which is defined thus:
where φE is the electric potential, and s is the path over which the integral is being taken.
Unfortunately, this definition has a caveat. From Maxwell's equations, it is clear that
is not always zero, and hence the scalar potential alone is insufficient to define the electric field exactly. As a result, one must resort to adding a correction factor, which is generally done by subtracting the time derivative of the A vector potential described below. Whenever the charges are quasistatic, however, this condition will be essentially met, so there will be few problems. (As a side note, by using the appropriate gauge transformations, one can define V to be zero and define E entirely as the negative time derivative of A, however, this is rarely done because a) it's a hassle and more important, b) it no longer satisfies the requirements of the Lorenz gauge and hence is no longer relativistically invariant).
From the definition of charge, it is trivial to show that the electric potential of a point charge as a function of position is:
where q is the point charge's charge, r is the position, and rq is the position of the point charge. The potential for a general distribution of charge ends up being:
where ρ is the charge density as a function of position, and r is the distance from the volume element
.
Note well that φ is a scalar, which means that it will add to other potential fields as a scalar. This makes it relatively easy to break complex problems down in to simple parts and add their potentials. Taking the definition of φ backwards, we see that the electric field is just the negative gradient (the del operator) of the potential. Or:
From this formula it is clear that E can be expressed in V/m (volts per meter).
Electromagnetic waves
A changing electromagnetic field propagates away from its origin in the form of a wave. These waves travel in vacuum at the speed of light and exist in a wide spectrum of wavelengths. Examples of the dynamic fields of electromagnetic radiation (in order of increasing frequency): radio waves, microwaves, light (infrared, visible light and ultraviolet), x-rays and gamma rays. In the field of particle physics this electromagnetic radiation is the manifestation of the electromagnetic interaction between charged particles.General field equations
As simple and satisfying as Coulomb's equation may be, it is not entirely correct in the context of classical electromagnetism. Problems arise because changes in charge distributions require a non-zero amount of time to be "felt" elsewhere (required by special relativity). Disturbances of the electric field due to a charge propagate at the speed of light.For the fields of general charge distributions, the retarded potentials can be computed and differentiated accordingly to yield Jefimenko's Equations.
Retarded potentials can also be derived for point charges, and the equations are known as the Liénard-Wiechert potentials. The scalar potential is:
where
is the point charge's charge and 
is the position. 
and 
are the position and velocity of the charge, respectively, as a function of retarded time. The vector potential is similar:
These can then be differentiated accordingly to obtain the complete field equations for a moving point particle.
See also
Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles.
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Electricity (from New Latin ēlectricus, "amberlike") is a general term for a variety of phenomena resulting from the presence and flow of electric charge. This includes many well-known physical phenomena such as lightning, electromagnetic fields and electric currents,
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magnetism is one of the phenomena by which materials exert attractive or repulsive forces on other materials. Some well known materials that exhibit easily detectable magnetic properties (called magnets) are nickel, iron and their alloys; however, all materials are influenced to
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Electrostatics (also known as static electricity) is the branch of physics that deals with the phenomena arising from what seem to be stationary electric charges. This includes phenomena as simple as the attraction of plastic wrap to your hand after you remove it from a
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Flavour in particle physics
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Coulomb's law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated as follows:
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- The magnitude of the electrostatic force between two points electric charges is directly proportional to the product of the magnitudes of each
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electric field. This electric field exerts a force on other electrically charged objects. The concept of electric field was introduced by Michael Faraday.
The electric field is a vector field with SI units of newtons per coulomb (N C−1
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The electric field is a vector field with SI units of newtons per coulomb (N C−1
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In physics and mathematical analysis, Gauss's law is the electrostatic application of the generalized Gauss's theorem giving the equivalence relation between any flux, e.g.
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Electric potential is the potential energy per unit of charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts. It is a scalar quantity.
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In physics, the electric dipole moment (or electric dipole for short) is a measure of the polarity of a system of electric charges.
In the simple case of two point charges, one with charge and one with charge , the electric dipole moment is:
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In the simple case of two point charges, one with charge and one with charge , the electric dipole moment is:
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Magnetostatics is the study of static magnetic fields. In electrostatics, the charges are stationary, whereas here, the currents are stationary. As it turns out magnetostatics is a good approximation even when the currents are not static as long as the currents do not
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magnetic field is a field that permeates space and which exerts a magnetic force on moving electric charges and magnetic dipoles. Magnetic fields surround electric currents, magnetic dipoles, and changing electric fields.
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Magnetic flux, represented by the Greek letter Φ (phi), is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field.
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The Biot-Savart Law is an equation in electromagnetism that describes the magnetic field vector B in terms of the magnitude and direction of the source electric current, the distance from the source electric current, and the magnetic permeability weighting factor.
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In physics, the magnetic moment or magnetic dipole moment is a measure of the strength of a magnetic source. In the simplest case of a current loop, the magnetic moment is defined as:
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Electric current is the flow (movement) of electric charge. The SI unit of electric current is the ampere (A), which is equal to a flow of one coulomb of charge per second.
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Definition
The amount of electric current (measured in amperes) through some surface, e.g...... Click the link for more information.
Lorentz force is the force exerted on a charged particle in an electromagnetic field. The particle will experience a force due to electric field of qE, and due to the magnetic field qv × B.
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Electromotive force (emf, ) is a term used to characterize electrical devices, such as voltaic cells, thermoelectric devices, electrical generators and transformers, and even resistors.
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For magnetic induction, see .
Electromagnetic induction is the production of voltage across a conductor situated in a changing magnetic field or a conductor moving through a stationary magnetic field...... Click the link for more information.
Faraday's law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop.
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Displacement current is a quantity related to changing electric field. It occurs in dielectric materials and also in free space.
In the particular case of when it occurs in free space, it is not believed to involve the motion of electric charge as is the case with
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In the particular case of when it occurs in free space, it is not believed to involve the motion of electric charge as is the case with
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For thermodynamic relations, see .
In electromagnetism, Maxwell's equations are a set of four equations that were first presented as a distinct group in 1884 by Oliver Heaviside in conjunction with Willard Gibbs...... Click the link for more information.
The electromagnetic field is a physical field produced by electrically charged objects. It affects the behaviour of charged objects in the vicinity of the field.
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Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. These components oscillate at right angles to each other and to the direction of propagation, and are in phase with each other.
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Electrical resistance is a measure of the degree to which an object opposes an electric current through it. The SI unit of electrical resistance is the ohm. Its reciprocal quantity is electrical conductance measured in siemens.
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Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. The most common form of charge storage device is a two-plate capacitor.
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inductance, or more accurately self-inductance of the circuit. The term was coined by Oliver Heaviside in February 1886. It is customary to use the symbol for inductance, possibly in honour of the physicist Heinrich Lenz.
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Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current (AC). Electrical impedance extends the concept of resistance to AC circuits, describing not only the relative magnitudes of the voltage and current, but also the
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A resonator is a device or system that exhibits resonance or resonant behavior. Many objects that use resonant effects are referred to simply as resonators. Examples of resonators are discussed in this article.
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theory of relativity, or simply relativity, refers specifically to two theories: Albert Einstein's special relativity and general relativity.
The term "relativity" was coined by Max Planck in 1908 to emphasize how special relativity (and later, general relativity)
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The term "relativity" was coined by Max Planck in 1908 to emphasize how special relativity (and later, general relativity)
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