| Articles about |
| Electromagnetism |
|---|
 |
Common symbols | ΦE |
|---|---|
| SI unit | Volt-meter (V m) |
| In SI base units | kg⋅m 3⋅s −3⋅A −1 |
| Dimension | ML3T−3I−1 |
In electromagnetism, electric flux is the measure of the electric field through a given surface, [1] 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.
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 "lines of flux" being radiated from a dot (the charge). These are called Gauss lines. [2] 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 directly 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 perpendicular to the flux lines. If the electric field is uniform, the electric flux passing through a surface of vector area A is
where E is the electric field (having units of V/m), E is its magnitude, A is the area of the surface, and θ is the angle between the electric field lines and the normal (perpendicular) to A.
For a non-uniform electric field, the electric flux dΦE through a small surface area dA is given by
(the electric field, E, multiplied by the component of area perpendicular to the field). The electric flux over a surface is therefore given by the surface integral:
where E is the electric field and dA is an infinitesimal area on the surface with an outward facing surface normal defining its direction.
For a closed Gaussian surface, electric flux is given by:
where
This relation is known as Gauss's law for electric fields in its integral form and it is one of Maxwell's equations.
While the electric flux is not affected by charges that are not within the closed surface, the net electric field, E can be affected by charges that lie outside the closed surface. While Gauss's law holds for all situations, it is most useful for "by hand" calculations when high degrees of symmetry exist in the electric field. Examples include spherical and cylindrical symmetry.
The [SI] unit of electric flux is the volt-meter (V·m), or Dimension is m⁰t‐¹a‐¹, or, equivalently, newton-meter squared per coulomb (N·m2·C−1). Thus, the unit of electric flux expressed in terms of SI base units is kg·m3·s−3·A−1. Its dimensional formula is .
In physics, the cross section is a measure of the probability that a specific process will take place in a collision of two particles. For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted σ (sigma) and is expressed in units of area, more specifically in barns. In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process.
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.
Flux describes any effect that appears to pass or travel through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface.
In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted Φ or ΦB. The SI unit of magnetic flux is the weber, and the CGS unit is the maxwell. Magnetic flux is usually measured with a fluxmeter, which contains measuring coils, and it calculates the magnetic flux from the change of voltage on the coils.
In physics, Gauss's law, also known as Gauss's flux theorem, is one of Maxwell's equations. It relates the distribution of electric charge to the resulting electric field.
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed.
Electrostatics is a branch of physics that studies slow-moving or stationary electric charges.
In mathematical physics, scalar potential, simply stated, describes the situation where the difference in the potential energies of an object in two different positions depends only on the positions, not upon the path taken by the object in traveling from one position to the other. It is a scalar field in three-space: a directionless value (scalar) that depends only on its location. A familiar example is potential energy due to gravity.
In physics, chemistry, a potential gradient is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because it leads to some form of flux.
An infinitesimal rotation matrix or differential rotation matrix is a matrix representing an infinitely small rotation.
In classical electromagnetism, polarization density is the vector field that expresses the volumetric 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.
Faraday's law of induction is a law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf). This phenomenon, known as electromagnetic induction, is the fundamental operating principle of transformers, inductors, and many types of electric motors, generators and solenoids.
In classical mechanics, the shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetrical body. This theorem has particular application to astronomy.
The Faraday paradox or Faraday's paradox is any experiment in which Michael Faraday's law of electromagnetic induction appears to predict an incorrect result. The paradoxes fall into two classes:
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, electric field, or magnetic field. It is an arbitrary closed surface S = ∂V used in conjunction with Gauss's law for the corresponding field by performing a surface integral, in order to calculate the total amount of the source quantity enclosed; e.g., 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.
Heaviside–Lorentz units constitute a system of units and quantities that extends the CGS with a particular set of equations that defines electromagnetic quantities, named for Oliver Heaviside and Hendrik Antoon Lorentz. They share with the CGS-Gaussian system that the electric constant ε0 and magnetic constant µ0 do not appear in the defining equations for electromagnetism, having been incorporated implicitly into the electromagnetic quantities. Heaviside–Lorentz units may be thought of as normalizing ε0 = 1 and µ0 = 1, while at the same time revising Maxwell's equations to use the speed of light c instead.
The method of image charges is a basic problem-solving tool in electrostatics. The name originates from the replacement of certain elements in the original layout with imaginary charges, which replicates the boundary conditions of the problem.
In physics, Gauss's law for magnetism is one of the four Maxwell's equations that underlie classical electrodynamics. It states that the magnetic field B has divergence equal to zero, in other words, that it is a solenoidal vector field. It is equivalent to the statement that magnetic monopoles do not exist. Rather than "magnetic charges", the basic entity for magnetism is the magnetic dipole.
In physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics that is equivalent to Newton's law of universal gravitation. It is named after Carl Friedrich Gauss. It states that the flux of the gravitational field over any closed surface is proportional to the mass enclosed. Gauss's law for gravity is often more convenient to work from than Newton's law.
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system: that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb-meter (C⋅m). The debye (D) is another unit of measurement used in atomic physics and chemistry.
