| Articles about |
| Electromagnetism |
|---|
 |
In electromagnetism, an electromagnetic wave (light) in vacuum travels at a finite speed (the speed of light c). The retarded time is the propagation delay between emission and observation, since it takes time for information to travel between emitter and observer. This arises due to causality.
Retarded time tr or t′ is calculated with a "speed-distance-time" calculation for EM fields.
If the EM field is radiated at position vector r′ (within the source charge distribution), and an observer at position r measures the EM field at time t, the time delay for the field to travel from the charge distribution to the observer is |r − r′|/c. Subtracting this delay from the observer's time t then gives the time when the field began to propagate, i.e. the retarded time t′. [1] [2]
The retarded time is:
(which can be rearranged to , showing how the positions and times of source and observer are causally linked).
A related concept is the advanced timeta, which takes the same mathematical form as above, but with a “+” instead of a “−”:
This is the time it takes for a field to propagate from originating at the present time t to a distance . Corresponding to retarded and advanced times are retarded and advanced potentials. [3]
The retarded position can be obtained from the current position of a particle by subtracting the distance it has travelled in the lapse from the retarded time to the current time. For an inertial particle, this position can be obtained by solving this equation:
where rc is the current position of the source charge distribution and v its velocity.
Perhaps surprisingly - electromagnetic fields and forces acting on charges depend on their history, not their mutual separation. [4] The calculation of the electromagnetic fields at a present time includes integrals of charge density ρ(r', tr) and current density J(r', tr) using the retarded times and source positions. The quantity is prominent in electrodynamics, electromagnetic radiation theory, and in Wheeler–Feynman absorber theory, since the history of the charge distribution affects the fields at later times.
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy.
An electromagnetic field is a physical field, mathematical functions of position and time, representing the influences on and due to electric charges. The field at any point in space and time can be regarded as a combination of an electric field and a magnetic field. Because of the interrelationship between the fields, a disturbance in the electric field can create a disturbance in the magnetic field which in turn affects the electric field, leading to an oscillation that propagates through space, known as an electromagnetic wave.
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, electric and magnetic circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar, etc. They describe how electric and magnetic fields are generated by charges, currents, and changes of the fields. The equations are named after the physicist and mathematician James Clerk Maxwell, who, in 1861 and 1862, published an early form of the equations that included the Lorentz force law. Maxwell first used the equations to propose that light is an electromagnetic phenomenon. The modern form of the equations in their most common formulation is credited to Oliver Heaviside.
A magnetic field is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism, diamagnetism, and antiferromagnetism, although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, electric currents, and electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function assigning a vector to each point of space, called a vector field.
An electric field is the physical field that surrounds electrically charged particles. Charged particles exert attractive forces on each other when their charges are opposite, and repulse each other when their charges are the same. Because these forces are exerted mutually, two charges must be present for the forces to take place. The electric field of a single charge describes their capacity to exert such forces on another charged object. These forces are described by Coulomb's law, which says that the greater the magnitude of the charges, the greater the force, and the greater the distance between them, the weaker the force. Thus, we may informally say that the greater the charge of an object, the stronger its electric field. Similarly, an electric field is stronger nearer charged objects and weaker further away. Electric fields originate from electric charges and time-varying electric currents. Electric fields and magnetic fields are both manifestations of the electromagnetic field, Electromagnetism is one of the four fundamental interactions of nature.
Electric potential is defined as the amount of work/energy needed per unit of electric charge to move the charge from a reference point to a specific point in an electric field. More precisely, the electric potential is the energy per unit charge for a test charge that is so small that the disturbance of the field under consideration is negligible. The motion across the field is supposed to proceed with negligible acceleration, so as to avoid the test charge acquiring kinetic energy or producing radiation. By definition, the electric potential at the reference point is zero units. Typically, the reference point is earth or a point at infinity, although any point can be used.
In physics, specifically electromagnetism, the Biot–Savart law is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current.
Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model. It is, therefore, a classical field theory. The theory provides a description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible. For small distances and low field strengths, such interactions are better described by quantum electrodynamics which is a quantum field theory.
An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric scalar potential and a magnetic vector potential into a single four-vector.
In classical electromagnetism, magnetic vector potential is the vector quantity defined so that its curl is equal to the magnetic field: . Together with the electric potential φ, 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 fields E and B, or equivalently in terms of the potentials φ and A. In more advanced theories such as quantum mechanics, most equations use potentials rather than fields.
In electromagnetism, the Lorenz gauge condition or Lorenz gauge is a partial gauge fixing of the electromagnetic vector potential by requiring The name is frequently confused with Hendrik Lorentz, who has given his name to many concepts in this field. The condition is Lorentz invariant. The Lorenz gauge condition does not completely determine the gauge: one can still make a gauge transformation where is the four-gradient and is any harmonic scalar function: that is, a scalar function obeying the equation of a massless scalar field.
In the physics of gauge theories, gauge fixing denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations. Any two detailed configurations in the same equivalence class are related by a certain transformation, equivalent to a shear along unphysical axes in configuration space. Most of the quantitative physical predictions of a gauge theory can only be obtained under a coherent prescription for suppressing or ignoring these unphysical degrees of freedom.
In electrodynamics, the Larmor formula is used to calculate the total power radiated by a nonrelativistic point charge as it accelerates. It was first derived by J. J. Larmor in 1897, in the context of the wave theory of light.
The Wheeler–Feynman absorber theory, named after its originators, the physicists Richard Feynman and John Archibald Wheeler, is a theory of electrodynamics based on a relativistic correct extension of action at a distance electron particles. The theory postulates no independent electromagnetic field. Rather, the whole theory is encapsulated by the Lorentz-invariant action of particle trajectories defined as
In electromagnetism, Jefimenko's equations give the electric field and magnetic field due to a distribution of electric charges and electric current in space, that takes into account the propagation delay of the fields due to the finite speed of light and relativistic effects. Therefore, they can be used for moving charges and currents. They are the particular solutions to Maxwell's equations for any arbitrary distribution of charges and currents.
The Liénard–Wiechert potentials describe the classical electromagnetic effect of a moving electric point charge in terms of a vector potential and a scalar potential in the Lorenz gauge. Stemming directly from Maxwell's equations, these describe the complete, relativistically correct, time-varying electromagnetic field for a point charge in arbitrary motion, but are not corrected for quantum mechanical effects. Electromagnetic radiation in the form of waves can be obtained from these potentials. These expressions were developed in part by Alfred-Marie Liénard in 1898 and independently by Emil Wiechert in 1900.
In electrodynamics, the retarded potentials are the electromagnetic potentials for the electromagnetic field generated by time-varying electric current or charge distributions in the past. The fields propagate at the speed of light c, so the delay of the fields connecting cause and effect at earlier and later times is an important factor: the signal takes a finite time to propagate from a point in the charge or current distribution to another point in space, see figure below.
In science, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. A weather map, with the surface temperature described by assigning a number to each point on the map, is an example of a scalar field. A surface wind map, assigning an arrow to each point on a map that describes the wind speed and direction at that point, is an example of a vector field, i.e. a 1-dimensional (rank-1) tensor field. Field theories, mathematical descriptions of how field values change in space and time, are ubiquitous in physics. For instance, the electric field is another rank-1 tensor field, while electrodynamics can be formulated in terms of two interacting vector fields at each point in spacetime, or as a single-rank 2-tensor field.
Weber electrodynamics is a theory of electromagnetism that preceded Maxwell electrodynamics and was replaced by it by the end of the 19th century. Weber electrodynamics is mainly based on the contributions of André-Marie Ampère, Carl Friedrich Gauss and Wilhelm Eduard Weber. In this theory, Coulomb's law becomes velocity and acceleration dependent. Weber electrodynamics is only applicable for electrostatics, magnetostatics and for the quasistatic approximation. Weber electrodynamics is not suitable for describing electromagnetic waves and for calculating the forces between electrically charged particles that move very rapidly or that are accelerated more than insignificantly.
Magnetic current is, nominally, a current composed of moving magnetic monopoles. It has the unit volt. The usual symbol for magnetic current is , which is analogous to for electric current. Magnetic currents produce an electric field analogously to the production of a magnetic field by electric currents. Magnetic current density, which has the unit V/m2, is usually represented by the symbols and . The superscripts indicate total and impressed magnetic current density. The impressed currents are the energy sources. In many useful cases, a distribution of electric charge can be mathematically replaced by an equivalent distribution of magnetic current. This artifice can be used to simplify some electromagnetic field problems. It is possible to use both electric current densities and magnetic current densities in the same analysis.
