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In electromagnetism, **electric flux** is the measure of the electric field through a given surface,^{ [1] } although an electric field in itself cannot flow. It is a way of describing the electric field strength at any distance from the charge causing the field.

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 a dot, the charge, radiating "lines of flux". 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 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 **S** is

where **E** is the electric field (having units of V/m), *E* is its magnitude, *S* is the area of the surface, and *θ* is the angle between the electric field lines and the normal (perpendicular) to **S**.

For a non-uniform electric field, the electric flux dΦ_{E} through a small surface area d**S** is given by

(the electric field, **E**, multiplied by the component of area perpendicular to the field). The electric flux over a surface **S** is therefore given by the surface integral:

where **E** is the electric field and d**S** is a differential area on the closed surface *S* with an outward facing surface normal defining its direction.

For a closed Gaussian surface, electric flux is given by:

where

**E**is the electric field,**S**is any closed surface,*Q*is the total electric charge inside the surface*S*,*ε*_{0}is the electric constant (a universal constant, also called the "permittivity of free space") (*ε*_{0}≈ 8.854 187 817... x 10^{−12}farads per meter (F·m^{−1}))

This relation is known as Gauss' law for electric field 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**, in the Gauss' Law equation, can be affected by charges that lie outside the closed surface. While Gauss' 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.

Electric flux has SI units of volt meters (V m), or, equivalently, newton meters squared per coulomb (N m^{2} C^{−1}). Thus, the SI base units of electric flux are kg·m^{3}·s^{−3}·A^{−1}. Its dimensional formula is [L^{3}MT^{−3}I^{−1}].

- Purcell, Edward, Morin, David; Electricity and Magnetism, 3rd Edition; Cambridge University Press, New York. 2013 ISBN 9781107014022.
- Browne, Michael, PhD; Physics for Engineering and Science, 2nd Edition; McGraw Hill/Schaum, New York; 2010. ISBN 0071613994

In physics, the **cross section** is a measure of the probability that a specific process will take place when some kind of radiant excitation intersects a localized phenomenon. For example, the Rutherford cross-section is a measure of probability that an alpha-particle will be deflected by a given angle during a collision with an atomic nucleus. Cross section is typically denoted *σ* (sigma) and is expressed in units of transverse area. 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.

**Maxwell's 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. 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.

A **magnetic field** is a vector 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 magnetic field that varies with location will exert a force on a range of non-magnetic materials by affecting the motion of their outer atomic electrons. Magnetic fields surround magnetized materials, and are created by electric currents such as those used in electromagnets, and by electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, they are described as a map assigning a vector to each point of space or, more precisely—because of the way the magnetic field transforms under mirror reflection—as a field of pseudovectors.

An **electric field** is the physical field that surrounds electrically-charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field for a system of charged particles. Electric fields originate from electric charges, or from time-varying magnetic fields. Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces of nature.

**Flux** describes any effect that appears to pass or travel through a surface or substance. A 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 Φ_{B}. 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 electronics, that evaluates the change of voltage in the measuring coils to calculate the measurement of magnetic flux.

In physics and electromagnetism, **Gauss's law**, also known as **Gauss's flux 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.

In vector calculus, the **divergence theorem**, also known as **Gauss's theorem** or **Ostrogradsky's theorem**, 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.

**Poisson's equation** is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate electrostatic or gravitational (force) field. It is a generalization of Laplace's equation, which is also frequently seen in physics. The equation is named after French mathematician and physicist Siméon Denis Poisson.

**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 electromagnetism, **displacement current density** is the quantity ∂* D*/∂

A **magnetic circuit** is made up of one or more closed loop paths containing a magnetic flux. The flux is usually generated by permanent magnets or electromagnets and confined to the path by magnetic cores consisting of ferromagnetic materials like iron, although there may be air gaps or other materials in the path. Magnetic circuits are employed to efficiently channel magnetic fields in many devices such as electric motors, generators, transformers, relays, lifting electromagnets, SQUIDs, galvanometers, and magnetic recording heads.

**Magnetic vector potential**, **A**, is the vector quantity in classical electromagnetism 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 physics, the **electric displacement field** 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}).

**Arc length** is the distance between two points along a section of a curve.

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, the 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.

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 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. Gauss's law for gravity is often more convenient to work from than is 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 units for electric dipole moment are coulomb-meter (C⋅m); however, a commonly used unit in atomic physics and chemistry is the debye (D).

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