In classical electromagnetism, magnetic vector potential (often called A) is the vector quantity 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.
Magnetic vector potential was first introduced by Franz Ernst Neumann and Wilhelm Eduard Weber in 1845 and in 1846, respectively. William Thomson also introduced vector potential in 1847, along with the formula relating it to the magnetic field.[1][2]
^Neumann, Franz Ernst (January 1, 1846). "Allgemeine Gesetze Der Inducirten Elektrischen Ströme (General laws of induced electrical currents)". Annalen der Physik. 143 (11): 31–34. doi:10.1002/andp.18461430103.
^Yang, ChenNing (2014). "The conceptual origins of Maxwell's equations and gauge theory". Physics Today. 67 (11): 45–51. Bibcode:2014PhT....67k..45Y. doi:10.1063/PT.3.2585.
and 24 Related for: Magnetic vector potential information
electromagnetism, magneticvectorpotential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field: ∇ × A = B...
potential. The electric potential and the magneticvectorpotential together form a four-vector, so that the two kinds of potential are mixed under Lorentz...
In vector calculus, a vectorpotential is a vector field whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar...
Magneticpotential may refer to: Magneticvectorpotential, the vector whose curl is equal to the magnetic B field Magnetic scalar potential, the magnetic...
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...
derivation starts from a multipole expansion of the vectorpotential. This leads to the definition of the magnetic dipole moment as: m = 1 2 ∭ V r × j ( r ) d...
Magnetic energy and electrostatic potential energy are related by Maxwell's equations. The potential energy of a magnet or magnetic moment m {\displaystyle...
Magnetic scalar potential, ψ, is a quantity in classical electromagnetism analogous to electric potential. It is used to specify the magnetic H-field...
t}}=0} . The magneticvectorpotential A in Coulomb gauge Longitudinal and transverse vector fields Stream function Conservative vector field This statement...
total magnetic current. M i {\displaystyle {\mathfrak {M}}^{\text{i}}} is the impressed magnetic current (energy source). The electric vectorpotential, F...
for a general discussion of magneticvectorpotential. See Feynman page 15-11 for a diagram of the magneticvectorpotential around a long thin solenoid...
with a permanent magnetic dipole moment. Dipoles, whether electric or magnetic, can be characterized by their dipole moment, a vector quantity. For the...
where bold letters represent vectors and E is the electric field vector; H is the magnetic field's auxiliary field vector or magnetizing field. This expression...
_{0}\mathbf {J} } where φ(r, t) is the electric potential and A(r, t) is the magneticvectorpotential, for an arbitrary source of charge density ρ(r,...
electric field cannot be described independently of the magnetic field. Given the magneticvectorpotential, A, defined so that B = ∇ × A {\displaystyle \mathbf...
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 _{E}=\mathbf {E}...
The E and B fields can be replaced by the magneticvectorpotential A and (scalar) electrostatic potential ϕ by E = − ∇ ϕ − ∂ A ∂ t B = ∇ × A {\displaystyle...
evidence that the ancient Chinese, Mayan, and potentially even Egyptian civilizations knew that the naturally magnetic mineral magnetite had attractive properties...
electric and magnetic fields are not rapidly changing, this can be neglected (see electrostatic approximation). The electric potential can be generalized...
relates current density to magnetic field. In special relativity theory, charge and current are combined into a 4-vector. Charge carriers which are free...
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...
electrostatic potential and a magneticvectorpotential The class of functions known as harmonic functions, which are the topic of study in potential theory...
other causes. Further, as they are vector fields, all magnetic and electric field vectors add together according to vector addition. For example, in optics...