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...

In classical electromagnetism, magnetic vector potential (often denoted A) is the vector quantity defined so that its curl is equal to the magnetic field...

electrostatics, the electrostatic field is a vector quantity expressed as the gradient of the electrostatic potential, which is a scalar quantity denoted by...

four-potential is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric scalar potential and...

{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...

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...

}{\partial t}}.\end{aligned}}} The vector potential, A given by this form may be interpreted as a generalized potential momentum per unit charge just as...

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...

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...

_{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,...

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...

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...

magnetic field and solve the remainder with the scalar potential method. Magnetic vector potential Vanderlinde 2005, pp. 194–199 Duffin, W.J. (1980). Electricity...

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...

potentials, and charges with currents, generally speaking. The most common description of the electromagnetic field uses two three-dimensional vector...

{A} }{\partial t}}\,\!} where A is the electromagnetic vector potential. This last potential expression in fact reduces Faraday's law to an identity...

operations on the above sorts of vectors. A vector space formed by geometric vectors is called a Euclidean vector space, and a vector space formed by tuples is...

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...

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...

term potential function may refer to: A mathematical function, whose values are given by a scalar potential or vector potential The electric potential, in...

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...

expressed in terms of the electric scalar potential φ {\displaystyle \varphi } and the magnetic vector potential A through the relations: E = − ∇ φ − ∂ A...

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...

is satisfied whenever a vector field v has only a vector potential component, because the definition of the vector potential A as: v = ∇ × A {\displaystyle...

curl from the vector potential. Another approach involves a general solution of the inhomogeneous wave equation for the vector potential in the case of...

\mathbf {u} } , also known as a solenoidal vector field, can always be represented as the curl of some vector potential A {\displaystyle {\boldsymbol {A}}} :...

magnetic vector potential such that B ( r ) = ∇ × A . {\displaystyle \mathbf {B} (\mathbf {r} )=\nabla \times \mathbf {A} .} Both of these potentials can be...

which is generally done by subtracting the time derivative of the A vector potential described below. Whenever the charges are quasistatic, however, this...

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...

Hertz vectors, or the Hertz vector potentials, are an alternative formulation of the electromagnetic potentials. They are most often introduced in electromagnetic...