# Electromagnetic induction

Electromagnetic induction is the production of a potential difference (voltage) across a conductor when it is exposed to a varying magnetic field. It is described mathematically by Faraday's law of induction, named after Michael Faraday who is generally credited with the discovery of induction in 1831. History A diagram of Faraday's iron ring apparatus. Electromagnetic induction was discovered independently by Michael Faraday and Joseph Henry in 1831; however, Faraday was the first to publish the results of his experiments.[2][3] In Faraday's first experimental demonstration of electromagnetic induction (August 29, 1831[4]), he wrapped two wires around opposite sides of an iron ring or "torus" (an arrangement similar to a modern toroidal transformer). Faraday explained electromagnetic induction using a concept he called lines of force. Faraday's law and the Maxwell–Faraday equation where is the electromotive force (EMF) and ΦB is the magnetic flux. the EMF on a wire loop is:

Electromagnetic radiation The electromagnetic waves that compose electromagnetic radiation can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This diagram shows a plane linearly polarized EMR wave propagating from left to right. The electric field is in a vertical plane and the magnetic field in a horizontal plane. The two types of fields in EMR waves are always in phase with each other with a fixed ratio of electric to magnetic field intensity. Electromagnetic radiation (EM radiation or EMR) is a form of radiant energy, propagating through space via electromagnetic waves and/or particles called photons. In classical physics, EMR is considered to be produced when charged particles are accelerated by forces acting on them. EMR carries energy—sometimes called radiant energy—through space continuously away from the source (this is not true of the near-field part of the EM field). Physics Theory Maxwell’s equations for EM fields far from sources

Electromagnetic field The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the electromagnetic field is described by Maxwell's equations and the Lorentz force law. From a classical perspective in the history of electromagnetism, the electromagnetic field can be regarded as a smooth, continuous field, propagated in a wavelike manner; whereas from the perspective of quantum field theory, the field is seen as quantized, being composed of individual particles.[citation needed] Structure of the electromagnetic field The electromagnetic field may be viewed in two distinct ways: a continuous structure or a discrete structure. Continuous structure Classically, electric and magnetic fields are thought of as being produced by smooth motions of charged objects.

Electrical resistance 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. The resistance (R) of an object is defined as the ratio of voltage across it (V) to current through it (I), while the conductance (G) is the inverse: may be most useful; this is called the "differential resistance". Introduction The hydraulic analogy compares electric current flowing through circuits to water flowing through pipes. In the hydraulic analogy, current flowing through a wire (or resistor) is like water flowing through a pipe, and the voltage drop across the wire is like the pressure drop that pushes water through the pipe. The voltage drop (i.e., difference in voltage between one side of the resistor and the other), not the voltage itself, provides the driving force pushing current through a resistor. Ohm's law where .

Permittivity A dielectric medium showing orientation of charged particles creating polarization effects. Such a medium can have a higher ratio of electric flux to charge (permittivity) than empty space In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how much electric field (more correctly, flux) is 'generated' per unit charge in that medium. More electric flux exists in a medium with a high permittivity (per unit charge) because of polarization effects. In SI units, permittivity ε is measured in farads per meter (F/m); electric susceptibility χ is dimensionless. where εr is the relative permittivity of the material, and ε0 = 8.8541878176.. × 10−12 F/m is the vacuum permittivity. Explanation Vacuum permittivity Its value is[1] where If

Electric field Electric field lines emanating from a point positive electric charge suspended over an infinite sheet of conducting material. Qualitative description An electric field that changes with time, such as due to the motion of charged particles producing the field, influences the local magnetic field. That is: the electric and magnetic fields are not separate phenomena; what one observer perceives as an electric field, another observer in a different frame of reference perceives as a mixture of electric and magnetic fields. Definition Electric Field Consider a point charge q with position (x,y,z). Notice that the magnitude of the electric field has dimensions of Force/Charge. Superposition Array of discrete point charges Electric fields satisfy the superposition principle. where Ei is the electric field created by the i-th point charge. where Qi is the electric charge of the i-th point charge, Continuum of charges Electrostatic fields Uniform fields

Electrical conductivity Definition Resistors or conductors with uniform cross-section A piece of resistive material with electrical contacts on both ends. where R is the electrical resistance of a uniform specimen of the material (measured in ohms, Ω) is the length of the piece of material (measured in metres, m) A is the cross-sectional area of the specimen (measured in square metres, m2). The reason resistivity is defined this way is that it makes resistivity an intrinsic property, unlike resistance. In a hydraulic analogy, passing current through a high-resistivity material is like pushing water through a pipe full of sand, while passing current through a low-resistivity material is like pushing water through an empty pipe. The above equation can be transposed to get Pouillet's law (named after Claude Pouillet): The resistance of a given material will increase with the length, but decrease with increasing cross-sectional area. The formula and General definition Conductivity is the inverse: 

Gaussian surface A cylindrical Gaussian surface is commonly used to calculate the electric charge of an infinitely long, straight, 'ideal' wire. A Gaussian surface is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, the electric field, or magnetic field.[1] It is an arbitrary closed surface S = ∂V (the boundary of a 3-dimensional region V) used in conjunction with Gauss's law for the corresponding field (Gauss's law, Gauss's law for magnetism, or Gauss's law for gravity) by performing a surface integral, in order to calculate the total amount of the source quantity enclosed, i.e. amount of gravitational mass as the source of the gravitational field or amount of electric charge as the source of the electrostatic field, or vice versa: calculate the fields for the source distribution. Gaussian surfaces are usually carefully chosen to exploit symmetries of a situation to simplify the calculation of the surface integral.

Magnetic field Magnetic field of an ideal cylindrical magnet with its axis of symmetry inside the image plane. The magnetic field is represented by magnetic field lines, which show the direction of the field at different points. In everyday life, magnetic fields are most often encountered as an invisible force created by permanent magnets which pull on ferromagnetic materials such as iron, cobalt or nickel and attract or repel other magnets. Magnetic fields are very widely used throughout modern technology, particularly in electrical engineering and electromechanics. The Earth produces its own magnetic field, which is important in navigation. Rotating magnetic fields are used in both electric motors and generators. History One of the first drawings of a magnetic field, by René Descartes, 1644. Three discoveries challenged this foundation of magnetism, though. Extending these experiments, Ampère published his own successful model of magnetism in 1825. Definitions, units, and measurement

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