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The electric potential at infinity is assumed to be zero. In electrodynamics, when time-varying fields are present, the electric field cannot be expressed only as a scalar potential. Instead, the electric field can be expressed as both the scalar electric potential and the magnetic vector potential. [2]
Many times in the use and calculation of electric and magnetic fields, the approach used first computes an associated potential: the electric potential, , for the electric field, and the magnetic vector potential, A, for the magnetic field. The electric potential is a scalar field, while the magnetic potential is a vector field.
The scalar potential is an example of a scalar field. Given a vector field F, the scalar potential P is defined such that: [1] = = (,,), where ∇P is the gradient of P and the second part of the equation is minus the gradient for a function of the Cartesian coordinates x, y, z. [a] In some cases, mathematicians may use a positive sign in front ...
Siméon Denis Poisson. 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 the corresponding electrostatic or gravitational (force) field.
An electric field (sometimes called E-field [1]) is a physical field that surrounds electrically charged particles.In classical electromagnetism, the electric field of a single charge (or group of charges) describes their capacity to exert attractive or repulsive forces on another charged object.
In the simplest case, the electric displacement field D resulting from an applied electric field E is = . More generally, the permittivity is a thermodynamic function of state. [1] It can depend on the frequency, magnitude, and direction of the applied field.
Position vector r is a point to calculate the electric field; r′ is a point in the charged object. Contrary to the strong analogy between (classical) gravitation and electrostatics, there are no "centre of charge" or "centre of electrostatic attraction" analogues. [citation needed] Electric transport
A uniform external electric field is supposed to point in the z-direction, and spherical polar coordinates are introduced so the potential created by this field is: = = . The sphere is assumed to be described by a dielectric constant κ , that is, D = κ ε 0 E , {\displaystyle \mathbf {D} =\kappa \varepsilon _{0}\mathbf {E} \,,} and inside ...