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Gauss's Law
In physics and electromagnetism, Gauss's law, also known as Gauss's flux theorem, (or sometimes simply called Gauss's theorem) is a law relating the distribution of electric charge to the resulting electric field. In its integral form, it states that the flux of the electric field out of an arbitrary closed surface is proportional to the electric charge enclosed by the surface, irrespective of how that charge is distributed. Even though the law alone is insufficient to determine the electric field across a surface enclosing any charge distribution, this may be possible in cases where symmetry mandates uniformity of the field. Where no such symmetry exists, Gauss's law can be used in its differential form, which states that the divergence of the electric field is proportional to the local density of charge. The law was first formulated by Joseph-Louis Lagrange in 1773, followed by Carl Friedrich Gauss in 1835, both in the context of the attraction of ellipsoids. It is one of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxwell Integral Gauss Sphere
Maxwell may refer to: People * Maxwell (surname), including a list of people and fictional characters with the name ** James Clerk Maxwell, mathematician and physicist * Justice Maxwell (other) * Maxwell baronets, in the Baronetage of Nova Scotia * Maxwell (footballer, born 1979), Brazilian forward * Maxwell (footballer, born 1981), Brazilian left-back * Maxwell (footballer, born 1986), Brazilian striker * Maxwell (footballer, born 1989), Brazilian left-back * Maxwell (footballer, born 1995), Brazilian forward * Maxwell (musician) (born 1973), American R&B and neo-soul singer * Maxwell (rapper) (born 1993), German rapper, member of rap band 187 Strassenbande * Maxwell Jacob Friedman (born 1997) AEW Professional wrestler * Maxwell Silva (born 1953), Sri Lankan Sinhala Catholic cleric, Archdiocese of Colombo, Auxiliary Bishop of Colombo Places United States * Maxwell, California * Maxwell, Indiana * Maxwell, Iowa * Maxwell, Nebraska * Maxwell, New Mexico * Maxwell, Te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Flux
In electromagnetism, electric flux is the measure of the electric field through a given surface, although an electric field in itself cannot flow. The electric field E can exert a force on an electric charge at any point in space. The electric field is the gradient of the potential. Overview An electric charge, such as a single electron in space, has an electric field surrounding it. In pictorial form, this electric field is shown as a dot, the charge, radiating "lines of flux". These are called Gauss lines.Purcell, pp. 5–6. Note that field lines are a graphic illustration of field strength and direction and have no physical meaning. The density of these lines corresponds to the electric field strength, which could also be called the electric flux density: the number of "lines" per unit area. Electric flux is proportional to the total number of electric field lines going through a surface. For simplicity in calculations, it is often convenient to consider a surface perpendicul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Integral
In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. Given a surface, one may integrate a scalar field (that is, a function of position which returns a scalar as a value) over the surface, or a vector field (that is, a function which returns a vector as value). If a region R is not flat, then it is called a ''surface'' as shown in the illustration. Surface integrals have applications in physics, particularly with the theories of classical electromagnetism. Surface integrals of scalar fields Assume that ''f'' is a scalar, vector, or tensor field defined on a surface ''S''. To find an explicit formula for the surface integral of ''f'' over ''S'', we need to parameterize ''S'' by defining a system of curvilinear coordinates on ''S'', like the latitude and longitude on a sphere. Let such a parameterization be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Constant
Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric constant, or the distributed capacitance of the vacuum. It is an ideal (baseline) physical constant. Its CODATA value is: : ( farads per meter), with a relative uncertainty of It is a measure of how dense of an electric field is "permitted" to form in response to electric charges, and relates the units for electric charge to mechanical quantities such as length and force. For example, the force between two separated electric charges with spherical symmetry (in the vacuum of classical electromagnetism) is given by Coulomb's law: :F_\text = \frac \frac Here, ''q''1 and ''q''2 are the charges, ''r'' is the distance between their centres, and the value of the constant fraction 1/4 \pi \varepsilon_0 (known as the Coulomb constant, ''k''e) is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Charge
In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is placed in an external electric field, its molecules gain electric dipole moment and the dielectric is said to be polarized. The electric dipole moment induced per unit volume of the dielectric material is called the electric polarization of the dielectric.''Introduction to Electrodynamics'' (3rd Edition), D.J. Griffiths, Pearson Education, Dorling Kindersley, 2007, ''McGraw Hill Encyclopaedia of Physics'' (2nd Edition), C.B. Parker, 1994, Polarization density also describes how a material responds to an applied electric field as well as the way the material changes the electric field, and can be used to calculate the forces that result from those interactions. It can be compared to magnetization, which is the measure of the corresponding ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Displacement Field
In physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "D" stands for "displacement", as in the related concept of displacement current in dielectrics. In free space, the electric displacement field is equivalent to flux density, a concept that lends understanding of Gauss's law. In the International System of Units (SI), it is expressed in units of coulomb per meter square (C⋅m−2). Definition In a dielectric material, the presence of an electric field E causes the bound charges in the material (atomic nuclei and their electrons) to slightly separate, inducing a local electric dipole moment. The electric displacement field "D" is defined as \mathbf \equiv \varepsilon_ \mathbf + \mathbf, where \varepsilon_ is the vacuum permittivity (also called permittivity of free space), and P is the (macroscopic) density of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divergence Theorem
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a theorem which relates the ''flux'' of a vector field through a closed surface to the ''divergence'' of the field in the volume enclosed. More precisely, the divergence theorem states that the surface integral of a vector field over a closed surface, which is called the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface. Intuitively, it states that "the sum of all sources of the field in a region (with sinks regarded as negative sources) gives the net flux out of the region". The divergence theorem is an important result for the mathematics of physics and engineering, particularly in electrostatics and fluid dynamics. In these fields, it is usually applied in three dimensions. However, it generalizes to any number of dimensions. In one dimension, it is equivalent to integration by parts. In two di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Calculus
In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve. The primary objects of study in differential calculus are the derivative of a function, related notions such as the differential, and their applications. The derivative of a function at a chosen input value describes the rate of change of the function near that input value. The process of finding a derivative is called differentiation. Geometrically, the derivative at a point is the slope of the tangent line to the graph of the function at that point, provided that the derivative exists and is defined at that point. For a real-valued function of a single real variable, the derivative of a function at a point generally determines the best linear approximation to the function at that point. Differential calculus and integral calculus are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral Calculus
In mathematics, an integral assigns numbers to Function (mathematics), functions in a way that describes Displacement (geometry), displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with Derivative, differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be interpreted as the signed area of the region in the plane that is bounded by the Graph of a function, graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are posi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Calculus
Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3. The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields, and fluid flow. Vector calculus was developed from quaternion analysis by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century, and most of the notation and terminology was established by Gibbs and Edwin Bidwell Wilson in their 1901 book, ''Vector Analysis''. In the conventional form using cross products, vector calculus does not generalize to higher dimensions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
