Soff-Quantenfeldtheorie.pdf. Electric field. Physical field surrounding an electric charge Electric fields are important in many areas of physics, and are exploited in electrical technology. In atomic physics and chemistry, for instance, the interaction in the electric field between the atomic nucleus and electrons is the force that holds these particles together in atoms. Similarly, the interaction in the electric field between atoms is the force responsible for chemical bonding that result in molecules. Description[edit] The electric field can be visualized with a set of lines whose direction at each point is the same as the field's, a concept introduced by Michael Faraday,[8] whose term 'lines of force' is still sometimes used. Mathematical formulation[edit] Electric fields are caused by electric charges, described by Gauss's law,[11] and time varying magnetic fields, described by Faraday's law of induction.[12] Together, these laws are enough to define the behavior of the electric field.
Electrostatics[edit] at position of:[13] and. Field line. Field lines depicting the electric field created by a positive charge (left), negative charge (center), and uncharged object (right). The figure at left shows the electric field lines of two equal positive charges. The figure at right shows the electric field lines of a dipole. Iron filings arrange themselves so as to approximately depict some magnetic field lines.
The magnetic field is created by a permanent magnet. Precise definition[edit] A vector field defines a direction at all points in space; a field line for that vector field may be constructed by tracing a topographic path in the direction of the vector field. More precisely, the tangent line to the path at each point is required to be parallel to the vector field at that point. A complete description of the geometry of all the field lines of a vector field is sufficient to completely specify the direction of the vector field everywhere. . , the correct result consistent with Coulomb's law for this case. Examples[edit] See also[edit]
Quantum field theory. Effective field theory. The renormalization group[edit] Presently, effective field theories are discussed in the context of the renormalization group (RG) where the process of integrating out short distance degrees of freedom is made systematic.
Although this method is not sufficiently concrete to allow the actual construction of effective field theories, the gross understanding of their usefulness becomes clear through a RG analysis. This method also lends credence to the main technique of constructing effective field theories, through the analysis of symmetries. If there is a single mass scale M in the microscopic theory, then the effective field theory can be seen as an expansion in 1/M. The construction of an effective field theory accurate to some power of 1/M requires a new set of free parameters at each order of the expansion in 1/M.
This technique is useful for scattering or other processes where the maximum momentum scale k satisfies the condition k/M≪1. Examples of effective field theories[edit] Sinusoidal plane-wave solutions of the electromagnetic wave equation. Sinusoidal plane-wave solutions are particular solutions to the electromagnetic wave equation. The treatment in this article is classical but, because of the generality of Maxwell's equations for electrodynamics, the treatment can be converted into the quantum mechanical treatment with only a reinterpretation of classical quantities (aside from the quantum mechanical treatment needed for charge and current densities).
The reinterpretation is based on the theories of Max Planck and the interpretations by Albert Einstein of those theories and of other experiments. The quantum generalization of the classical treatment can be found in the articles on Photon polarization and Photon dynamics in the double-slit experiment. Explanation[edit] Experimentally, every light signal can be decomposed into a spectrum of frequencies and wavelengths associated with sinusoidal solutions of the wave equation.
Plane waves[edit] for the electric field and for the magnetic field, where k is the wavenumber, where and. Elliptical polarization. Other forms of polarization, such as circular and linear polarization, can be considered to be special cases of elliptical polarization. Mathematical description of elliptical polarization[edit] The classical sinusoidal plane wave solution of the electromagnetic wave equation for the electric and magnetic fields is (cgs units) for the magnetic field, where k is the wavenumber, is the angular frequency of the wave propagating in the +z direction, and is the speed of light.
Here is the amplitude of the field and is the normalized Jones vector. Traces out an ellipse in the x-y plane. And where . The semi-major axis makes with the x-axis. If , the wave is linearly polarized. ) oriented at an angle. . , and the other in the y direction with an amplitude . . Becomes negative from zero, the line evolves into an ellipse that is being traced out in the clockwise direction; this corresponds to Right-Handed Elliptical Polarization. , i.e. , the wave is left-circularly polarized, and when See also[edit]
Circular polarization. The electric field vectors of a traveling circularly polarized electromagnetic wave. In electrodynamics the strength and direction of an electric field is defined by what is called an electric field vector. In the case of a circularly polarized wave, as seen in the accompanying animation, the tip of the electric field vector, at a given point in space, describes a circle as time progresses. If the wave is frozen in time, the electric field vector of the wave describes a helix along the direction of propagation. Circular polarization is a limiting case of the more general condition of elliptical polarization. The phenomenon of polarization arises as a consequence of the fact that light behaves as a two-dimensional transverse wave. General description[edit] Right-handed/clockwise circularly polarized light displayed with and without the use of components.
Left-handed/counter-clockwise circularly polarized light displayed with and without the use of components. FM radio[edit] where Here If and. Photon polarization. Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. Individual photon eigenstates have either right or left circular polarization. A photon that is in a superposition of eigenstates can have linear, circular, or elliptical polarization. The description of photon polarization contains many of the physical concepts and much of the mathematical machinery of more involved quantum descriptions, such as the quantum mechanics of an electron in a potential well, and forms a fundamental basis for an understanding of more complicated quantum phenomena. Much of the mathematical machinery of quantum mechanics, such as state vectors, probability amplitudes, unitary operators, and Hermitian operators, emerge naturally from the classical Maxwell's equations in the description.
Polarization of classical electromagnetic waves[edit] Polarization states[edit] Linear polarization[edit] Effect of a polarizer on reflection from mud flats. . Electromagnetic wave equation. Where ), and permittivity ( ), and ∇2 is the Laplace operator. In a vacuum, c = c0 = 299,792,458 meters per second, which is the speed of light in free space.[1] The electromagnetic wave equation derives from Maxwell's equations. It should also be noted that in most older literature, B is called the magnetic flux density or magnetic induction. The origin of the electromagnetic wave equation[edit] In his 1864 paper titled A Dynamical Theory of the Electromagnetic Field, Maxwell utilized the correction to Ampère's circuital law that he had made in part III of his 1861 paper On Physical Lines of Force. In Part VI of his 1864 paper titled Electromagnetic Theory of Light,[2] Maxwell combined displacement current with some of the other equations of electromagnetism and he obtained a wave equation with a speed equal to the speed of light.
To obtain the electromagnetic wave equation in a vacuum using the modern method, we begin with the modern 'Heaviside' form of Maxwell's equations. And . P. Relativistic electromagnetism. Einstein's motivation[edit] In 1953 Albert Einstein wrote to the Cleveland Physics Society on the occasion of a commemoration of the Michelson–Morley experiment. In that letter he wrote:[1] What led me more or less directly to the special theory of relativity was the conviction that the electromotive force acting on a body in motion in a magnetic field was nothing else but an electric field. This statement by Einstein reveals that he investigated spacetime symmetries to determine the complementarity of electric and magnetic forces.
Introduction[edit] Purcell argued that the question of an electric field in one inertial frame of reference, and how it looks from a different reference frame moving with respect to the first, is crucial to understand fields created by moving sources. Alternatively, introductory treatments of magnetism introduce the Biot–Savart law, which describes the magnetic field associated with an electric current.
Uniform electric field — simple analysis[edit] and For. Lorentz force. Force acting on charged particles in electric and magnetic fields Lorentz force acting on fast-moving charged particles in a bubble chamber. Positive and negative charge trajectories curve in opposite directions. In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields.
A particle of charge q moving with a velocity v in an electric field E and a magnetic field B experiences a force of (in SI units[1][2]). It says that the electromagnetic force on a charge q is a combination of a force in the direction of the electric field E proportional to the magnitude of the field and the quantity of charge, and a force at right angles to the magnetic field B and the velocity v of the charge, proportional to the magnitude of the field, the charge, and the velocity. Lorentz force law as the definition of E and B[edit] Equation[edit] Charged particle[edit] where . By eliminating. Wheeler–Feynman absorber theory. The Wheeler–Feynman absorber theory (also called the Wheeler–Feynman time-symmetric theory) is an interpretation of electrodynamics derived from the assumption that the solutions of the electromagnetic field equations must be invariant under time-reversal symmetry, as are the field equations themselves. Indeed, there is no apparent reason for the time-reversal symmetry breaking which singles out a preferential time direction and thus makes a distinction between past and future.
A time-reversal invariant theory is more logical and elegant. Another key principle, resulting from this interpretation and reminiscent of Mach's principle due to Tetrode, is that elementary particles are not self-interacting. This immediately removes the problem of self-energies. This theory is named after its originators, the late physicists Richard Feynman and John Archibald Wheeler. T-symmetry and causality[edit] and point , which will arrive at point at the instant (here Then they observed that, if the relation T.
Static forces and virtual-particle exchange. The virtual-particle description of static forces is capable of identifying the spatial form of the forces, such as the inverse-square behavior in Newton's law of universal gravitation and in Coulomb's law. It is also able to predict whether the forces are attractive or repulsive for like bodies. As with any physical theory, there are limits to the validity of the virtual particle picture. The virtual-particle formulation is derived from a method known as perturbation theory which is an approximation assuming interactions are not too strong, and was intended for scattering problems, not bound states such as atoms. For the strong force binding quarks into nucleons at low energies, perturbation theory has never been shown to yield results in accord with experiments,[2] thus, the validity of the "force-mediating particle" picture is questionable.
Similarly, for bound states the method fails.[3] In these cases the physical interpretation must be re-examined. Classical forces[edit] is to mass. Darwin Lagrangian. The Darwin Lagrangian (named after Charles Galton Darwin, grandson of the biologist) describes the interaction to order between two charged particles in a vacuum and is given by[1] where the free particle Lagrangian is and the interaction Lagrangian is where the Coulomb interaction is and the Darwin interaction is Here q1 and q2 are the charges on particles 1 and 2 respectively, m1 and m2 are the masses of the particles, v1 and v2 are the velocities of the particles, c is the speed of light, r is the vector between the two particles, and is the unit vector in the direction of r. The free Lagrangian is the Taylor expansion of free Lagrangian of two relativistic particles to second order in v. Derivation of the Darwin interaction in a vacuum[edit] The relativistic interaction Lagrangian for a particle with charge q interacting with an electromagnetic field is[2] where u is the relativistic velocity of the particle.
The vector potential in the Coulomb gauge is described by[3] (Gaussian units) where. Biot–Savart law. In physics, particularly electromagnetism, the Biot–Savart law (/ˈbiːoʊ səˈvɑr/ or /ˈbjoʊ səˈvɑr/)[1] 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.[2] It is named for Jean-Baptiste Biot and Félix Savart who discovered this relationship in 1820. Equation[edit] Electric currents (along closed curve)[edit] The Biot–Savart law is used for computing the resultant magnetic field B at position r generated by a steady current I (for example due to a wire): a continual flow of charges which is constant in time and the charge neither accumulates nor depletes at any point. The law is a physical example of a line integral: evaluated over the path C the electric currents flow.
The equation in SI units is[3] is the unit vector of r. Maxwell's equations. Equations describing classical electromagnetism 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, and electric 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. [note 1] 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.
The equations have two major variants. History of the equations[edit] Conceptual descriptions[edit] Gauss's law[edit] Gauss's law for magnetism[edit] Faraday's law[edit] Ampère's law with Maxwell's addition[edit] Key to the notation[edit] Jefimenko's equations. Liénard–Wiechert potential. Electromagnetic radiation.