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Mathematical concept in vector calculus
In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar
Vector_potential
Quantity in electromagnetism
In classical electromagnetism, magnetic vector potential (often denoted A) is the vector quantity defined so that its curl is equal to the magnetic field
Magnetic_vector_potential
Line integral of the electric field
potential. The electric potential and the magnetic vector potential together form a four-vector, so that the two kinds of potential are mixed under Lorentz
Electric_potential
Relativistic vector field
four-potential is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric scalar potential and
Electromagnetic four-potential
Electromagnetic_four-potential
Vector field that is the gradient of some function
In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property
Conservative_vector_field
Type of electrical device
general discussion of magnetic vector potential. See Feynman page 15-11 for a diagram of the magnetic vector potential around a long thin solenoid which
Toroidal inductors and transformers
Toroidal_inductors_and_transformers
Electromagnetic quantum-mechanical effect in regions of zero magnetic and electric field
be viewed as generated by a solenoid's vector potential acting on the electron or the electron's vector potential acting on the solenoid or the electron
Aharonov–Bohm_effect
Flow of magnetic monopole charge
{M}}^{\text{i}}} is the impressed magnetic current (energy source). The electric vector potential, F, is computed from the magnetic current density, M i {\displaystyle
Magnetic_current
Species of mosquito
August 2020). "Laboratory transmission potential of British mosquitoes for equine arboviruses". Parasites & Vectors. 13 (1) 413. doi:10.1186/s13071-020-04285-x
Culiseta_annulata
Property of space that quantifies the magnetic influence at a given location
magnetic vector potential A, and the electric scalar potential φ, are defined such that: Definition of the vector A and scalar φ potentials (vector form, SI
Magnetic_field
Foundational law of classical magnetism
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
Gauss's_law_for_magnetism
When potential energy difference depends only on displacement
confusion with vector potential). The scalar potential is an example of a scalar field. Given a vector field F, the scalar potential P is defined such
Scalar_potential
Currently unrealized ability
pushing it over the edge. In physics, a potential may refer to the scalar potential or to the vector potential. In either case, it is a field defined in
Potential
Energy held by an object because of its position relative to other objects
and defines a scalar potential field. In this case, the force can be defined as the negative of the vector gradient of the potential field. If the work
Potential_energy
Function for incompressible divergence-free flows in two dimensions
\mathbf {u} } , also known as a solenoidal vector field, can always be represented as the curl of some vector potential A {\displaystyle {\boldsymbol {A}}} :
Stream_function
Type of potential in electrodynamics
_{0}\mathbf {J} } where φ(r, t) is the electric potential and A(r, t) is the magnetic vector potential, for an arbitrary source of charge density ρ(r,
Retarded_potential
Electromagnetic effect of point charges
Liénard–Wiechert potentials describe the classical electromagnetic effect of a moving electric point charge in terms of a vector potential and a scalar potential in
Liénard–Wiechert_potential
Quantization giving rise to photons
time-dependent vector fields that in vacuum depend on a third vector field A ( r , t ) {\displaystyle \mathbf {A} (\mathbf {r} ,t)} (the vector potential), as well
Quantization of the electromagnetic field
Quantization_of_the_electromagnetic_field
Formulations of electromagnetism
potentials, and charges with currents, generally speaking. The most common description of the electromagnetic field uses two three-dimensional vector
Mathematical descriptions of the electromagnetic field
Mathematical_descriptions_of_the_electromagnetic_field
Vector field with zero divergence
In vector calculus and differential equations, a divergence free vector field is a vector field v with divergence zero at all points in the field: ∇ ⋅
Solenoidal_vector_field
Magnetic analog of electric potential valid outside materials
magnetic field and solve the remainder with the scalar potential method. Magnetic vector potential Vanderlinde 2005, pp. 194–199 Duffin, W.J. (1980). Electricity
Magnetic_scalar_potential
Branch of physics about magnetism in systems with steady electric currents
magnetic potential. The value of B {\displaystyle \mathbf {B} } can be found from the magnetic potential. The magnetic field can be derived from the vector potential
Magnetostatics
Assignment of a vector to each point in a subset of Euclidean space
In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space ℝn. A vector field
Vector_field
Branch of theoretical physics
which is generally done by subtracting the time derivative of the A vector potential described below. Whenever the charges are quasistatic, however, this
Classical_electromagnetism
Difference in electric potential between two points in space
also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a
Voltage
Local rate of change in potential with respect to displacement
{A} }{\partial t}}\,\!} where A is the electromagnetic vector potential. This last potential expression in fact reduces Faraday's law to an identity
Potential_gradient
Procedure of coping with redundant degrees of freedom in physical field theories
expressed in terms of the electric scalar potential φ {\displaystyle \varphi } and the magnetic vector potential A through the relations: E = − ∇ φ − ∂ A
Gauge_fixing
Ways of writing certain laws of physics
covariant four-vector containing the electric potential (also called the scalar potential) ϕ and magnetic vector potential (or vector potential) A, as follows:
Covariant formulation of classical electromagnetism
Covariant_formulation_of_classical_electromagnetism
Law of classical electromagnetism
curl from the vector potential. Another approach involves a general solution of the inhomogeneous wave equation for the vector potential in the case of
Biot–Savart_law
Electromagnetic equations describing superconductors
be combined into a single "London Equation" in terms of a specific vector potential A s {\displaystyle \mathbf {A} _{\rm {s}}} which has been gauge fixed
London_equations
Force acting on charged particles in electric and magnetic fields
E and B fields can be replaced by the magnetic vector potential A and (scalar) electrostatic potential ϕ by E = − ∇ ϕ − ∂ A ∂ t B = ∇ × A {\displaystyle
Lorentz_force
Physical field surrounding an electric charge
magnetic field. Given the magnetic vector potential, A, defined so that 𝐁=∇×𝐀, one can still define an electric potential φ such that: 𝐄=−∇φ−∂𝐀∂t, where
Electric_field
Topics referred to by the same term
term potential function may refer to: A mathematical function, whose values are given by a scalar potential or vector potential The electric potential, in
Potential_function
Formulation of electromagnetic potentials
Hertz vectors, or the Hertz vector potentials, are an alternative formulation of the electromagnetic potentials. They are most often introduced in electromagnetic
Hertz_vector
German physicist and mineralogist (1798–1895)
In electromagnetism, he is credited for introducing the magnetic vector potential. In A Treatise on Electricity and Magnetism of 1873, James Clerk Maxwell
Franz_Ernst_Neumann
Concept in the physics of electromagnetism
In electromagnetism, the magnetic moment or magnetic dipole moment is a vector quantity which characterizes the strength and orientation of a magnet or
Magnetic_moment
Fundamental interaction between charged particles
potential energy and momentum. In this case, the electromagnetic field is represented by the electric potential, V, and the magnetic vector potential
Electromagnetism
Gauge fixing of electro magnetic potential
(after Ludvig Lorenz) is a partial gauge fixing of the electromagnetic vector potential by requiring ∂ μ A μ = 0 {\displaystyle \partial _{\mu }A^{\mu }=0}
Lorenz_gauge_condition
Potential energy that results from conservative Coulomb forces
dr' is the displacement vector in a curve from the reference position rref to the final position r. The electrostatic potential energy can also be defined
Electric_potential_energy
Two-dimensional vector image file format
edited with text editors or vector graphics editors, and are rendered by most web browsers. SVG can include JavaScript, potentially leading to cross-site scripting
SVG
Topics referred to by the same term
Scalar potential, a scalar field whose gradient is a given vector field Vector potential, a vector field whose curl is a given vector field Potential function
Potential_(disambiguation)
Certain vector fields are the sum of an irrotational and a solenoidal vector field
theorem of vector calculus states that certain differentiable vector fields can be resolved into the sum of an irrotational (curl-free) vector field and
Helmholtz_decomposition
Property of a mass in motion
object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity (also a vector quantity), then
Momentum
Equation used to calculate the electromigration of ions in a fluid
{\displaystyle \phi } is the electric potential and A {\displaystyle {\bf {A}}} is the magnetic vector potential. Therefore, the Nernst–Planck equation
Nernst–Planck_equation
Surface integral of the magnetic field
_{S}\mathbf {B} \cdot d\mathbf {S} .} From the definition of the magnetic vector potential A and the fundamental theorem of the curl the magnetic flux may also
Magnetic_flux
Elementary particle or quantum of light
designed to detect effects caused by the galactic vector potential. Although the galactic vector potential is large because the galactic magnetic field exists
Photon
Superconductivity theory
charge of a Cooper pair, A {\displaystyle \mathbf {A} } is the magnetic vector potential, and H = ∇ × A {\displaystyle \mathbf {H} =\nabla \times \mathbf {A}
Ginzburg–Landau_theory
Measure of directional electromagnetic energy flux
In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or
Poynting_vector
Topics referred to by the same term
Magnetic potential may refer to: Magnetic vector potential, the vector whose curl is equal to the magnetic B field Magnetic scalar potential, the magnetic
Magnetic_potential
Region in space where every point is at the same potential
same potential. This usually refers to a scalar potential (in that case it is a level set of the potential), although it can also be applied to vector potentials
Equipotential
Measure of magnetic field topology
H M {\displaystyle H^{\mathbf {M} }} is the helicity of a magnetic vector potential A {\displaystyle {\mathbf {A} }} where ∇ × A = B {\displaystyle \nabla
Magnetic_helicity
Energy from the work of a magnetic force
current density field and A {\displaystyle \mathbf {A} } is the magnetic vector potential. This is analogous to the electrostatic energy expression 1 2 ∫ ρ ϕ
Magnetic_energy
Concept of vector calculus
In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0);
Closed and exact differential forms
Closed_and_exact_differential_forms
Lowest energy state in quantum electrodynamics
of the electromagnetic field begins by introducing a vector potential A and a scalar potential V to represent the electric field E and magnetic field
QED_vacuum
Study of still or slow electric charges
the electric field is the negative gradient of the electric potential, as well as vector calculus identities in a way that resembles integration by parts
Electrostatics
Effective theory of gravity
gravitational potential. The vector field A→ is interpreted as the gravito-magnetic vector potential. It is analogous to the magnetic vector potential in electromagnetism
Non-relativistic general relativity
Non-relativistic_general_relativity
Electromagnetic effect in physics
gauge the electromagnetic vector potential is A = ( 0 , B x , 0 ) {\displaystyle \mathbf {A} =(0,Bx,0)} and the scalar potential is ϕ = 0 {\displaystyle
Quantum_Hall_effect
Equations describing classical electromagnetism
fields, and indirectly in terms of the electrical potential φ and the vector potential A. Potentials were introduced as a convenient way to solve the homogeneous
Maxwell's_equations
Vector in relativity
In special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) is an element of a four-dimensional vector space object with four components
Four-vector
Mechanism that explains the generation of mass for gauge bosons
varying condensate in the gauge where the vector potential is zero. In the gauge where A is zero, the potential energy density in the condensate is the
Higgs_mechanism
Electromagnetic phenomenon
arbitrary electrostatic potential Φ. This term will dominate at large distances if there is no net charge (and if p≠0). The vector potential Adip at position
Dipole
Conserved physical quantity; rotational analogue of linear momentum
where e is the electric charge of the particle and A the magnetic vector potential of the electromagnetic field. The gauge-invariant angular momentum
Angular_momentum
Electrical action produced by a non-electrical source
basic understanding of induced emf is based on the vector potential rather than the scalar potential), and consider it as a load element in Kirchhoff's
Electromotive_force
Unified field theory
usual four dimensions of space and time; a 4-vector Aμ identified with the electromagnetic vector potential; and a scalar field ϕ. Then decompose the 5D
Kaluza–Klein_theory
Circulation density in a vector field
In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional
Curl_(mathematics)
Hypothetical particle with one magnetic pole
locally define the vector potential such that the curl of the vector potential 𝐀 equals the magnetic field 𝐁. However, the vector potential cannot be defined
Magnetic_monopole
Equations of motion for viscous fluids
the variable of interest, the existence of the stream function or vector potential is necessary by the Helmholtz theorem. Further, to determine fluid
Navier–Stokes_equations
Flow of electric charge
rate at which charge passes through a chosen unit area. It is defined as a vector whose magnitude is the current per unit cross-sectional area. As discussed
Electric_current
Process in quantum optics
and the Power-Zienau unitary transformation eliminating the quantum vector potential in the minimum-coupling Hamiltonian transforms the Hamiltonian exactly
Superradiant_phase_transition
Method to include magnetic fields in tight-binding models
tightly-bound electrons in the presence of a slowly varying magnetic vector potential. Specifically, the Peierls substitution modifies the hopping integrals
Peierls_substitution
Fundamental study of potential theory
dm(\mathbf {r} ).} The potential can be expanded in a series of Legendre polynomials. Represent the points x and r as position vectors relative to the center
Gravitational_potential
Lattice field theory with only spatial discretization
d-dimensional lattice. Following Wilson, the spatial components of the vector potential are replaced with Wilson lines over the edges, but the time component
Hamiltonian lattice gauge theory
Hamiltonian_lattice_gauge_theory
Vector operator in vector calculus
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters
Divergence
Quantization of cyclotron orbits
electromagnetic vector potential A {\textstyle \mathbf {A} } (in position space A ^ = A {\textstyle {\hat {\mathbf {A} }}=\mathbf {A} } ). The vector potential is
Landau_levels
Physical quantity in electromagnetism
the electric potential (which can be chosen to satisfy Poisson's equation) and A is a vector potential (i.e. magnetic vector potential, not to be confused
Displacement_current_density
Vector field representing a mass's effect on surrounding space
physics, a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space
Gravitational_field
Quantum operator for the sum of energies of a system
charge q in an electromagnetic field, described by the scalar potential ϕ and vector potential 𝐀, there are two parts to the Hamiltonian to substitute for
Hamiltonian (quantum mechanics)
Hamiltonian_(quantum_mechanics)
Quantum field theory
identity matrix (matching the size of the generators), Aμa is the vector potential, and g is the coupling constant. In four dimensions, the coupling constant
Yang–Mills_theory
Introductory article
static electricity to electromagnetism, we have a second potential, the magnetic vector potential A, which can also undergo gauge transformations. These
Introduction_to_gauge_theory
Electromagnetic property of matter
magnetism Magnetic dipole Magnetic flux Magnetic scalar potential Magnetic vector potential Magnetization Permeability Right-hand rule Electrodynamics
Electric_charge
Physical theory with fields invariant under the action of local "gauge" Lie groups
that any vector field whose curl vanishes—and can therefore normally be written as a gradient of a function—could be added to the vector potential without
Gauge_theory
Physical quantities taking values at each point in space and time
field or field quantity is a physical quantity – represented by a scalar, vector, spinor, or tensor – that has a value for each point in space and time.
Field_(physics)
Fundamental physical law of electromagnetism
{r_{12}=r_{1}-r_{2}} } is the displacement vector between the charges, r ^ 12 {\textstyle {\hat {\mathbf {r} }}_{12}} a unit vector pointing from q 2 {\textstyle q_{2}}
Coulomb's_law
Measure of electric field through surface
electric field is uniform, the electric flux passing through a surface of vector area A is Φ E = E ⋅ A = E A cos θ , {\displaystyle \Phi _{\text{E}}=\mathbf
Electric_flux
SI derived unit of power
performed when a current of one ampere (A) flows across an electrical potential difference of one volt (V), meaning the watt is equivalent to the volt-ampere
Watt
Mathematical object that describes the electromagnetic field in spacetime
=\mathbf {B} } ( A {\displaystyle \mathbf {A} } is a vector potential for the solenoidal vector field B {\displaystyle \mathbf {B} } ). The electric and
Electromagnetic_tensor
Set of methods for supervised statistical learning
In machine learning, a support vector machine (SVM) or support vector network is a supervised max-margin model with associated learning algorithms that
Support_vector_machine
Equations in quantum field theory
parameter; V {\displaystyle V} the electrochemical potential; A x {\displaystyle A_{x}} the magnetic vector potential; and ξ {\displaystyle \xi } the superconducting
Time-dependent Ginzburg–Landau theory
Time-dependent_Ginzburg–Landau_theory
Biotechnology for gene delivery
A viral vector is a modified virus designed to deliver genetic material into cells. This process can be performed inside an organism or in cell culture
Viral_vector
Magnetic analogue of the electric dipole
Conventionally, the derivation starts from a multipole expansion of the vector potential. This leads to the definition of the magnetic dipole moment as: m =
Magnetic_dipole
Quantum field that enables consistent quantization
fields is the photon, which is usually described by a four-component vector potential Aμ, even if light has only two allowed polarizations in the vacuum
Ghost_(physics)
Law of electrical current and voltage
points is directly proportional to the voltage (the difference of electric potential) across the two points. Introducing the constant of proportionality, the
Ohm's_law
Hypothetical particle dual to the photon
singularity is to include a second four-vector potential, called dual photon, in addition to the usual four-vector potential, photon. Additionally, it is found
Dual_photon
Complex vector of electromagnetic fields
{G} } is any complex vector field with the non-vanishing rotation, or it is a vector potential for the Riemann–Silberstein vector. While having the wave
Riemann–Silberstein_vector
Italian chemist and physicist (1745–1827)
from a series of illnesses which began in 1823. The SI unit of electric potential is named the volt in his honour. Volta was born in Como, a town in northern
Alessandro_Volta
Rate at which electrical energy is transferred by an electric circuit
quantities as vectors. Real power is represented as a horizontal vector and reactive power is represented as a vertical vector. The apparent power vector is the
Electric_power
Elliptic partial differential equation
also depends on the magnetic vector potential A, which must be independently computed. See Maxwell's equation in potential formulation for more on φ and
Poisson's_equation
Lowest possible energy of a quantum system or field
and creation operators for the mode with wave vector k and polarization λ. This gives the vector potential for a plane wave mode of the field. The condition
Zero-point_energy
Quantum of electromagnetic flux
(~100 nm), is quantized because of the phase properties of the magnetic vector potential in quantum electrodynamics, see magnetic flux quantum for details.
Fluxon
Theorem in quantum mechanics
(1970). An enclosed flux Φ {\displaystyle \Phi } corresponds to a vector potential A ( r ) {\displaystyle \mathbf {A} (\mathbf {r} )} inside the annulus
Byers–Yang_theorem
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VECTOR POTENTIAL
VECTOR POTENTIAL
VECTOR POTENTIAL
VECTOR POTENTIAL
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