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In short, an electric potential is the electric potential energy per unit charge. This value can be calculated in either a static (time-invariant) or a dynamic (time-varying) electric field at a specific time with the unit joules per coulomb (J⋅C −1) or volt (V). The electric potential at infinity is assumed to be zero.
The following outline of proof states the derivation from the definition of electric potential energy and Coulomb's law to this formula. Outline of proof The electrostatic force F acting on a charge q can be written in terms of the electric field E as F = q E , {\displaystyle \mathbf {F} =q\mathbf {E} ,}
The coefficients of potential are the coefficients p ij. φ i should be correctly read as the potential on the i -th conductor, and hence " p 21 {\displaystyle p_{21}} " is the p due to charge 1 on conductor 2.
Position vectors r and r′ used in the calculation. The starting point is Maxwell's equations in the potential formulation using the Lorenz gauge: =, = 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, t) and current density J(r, t), and is the D'Alembert operator. [2]
the total electric charge density (total charge per unit volume), ρ, and; the total electric current density (total current per unit area), J. The universal constants appearing in the equations (the first two ones explicitly only in the SI formulation) are: the permittivity of free space, ε 0, and; the permeability of free space, μ 0, and
One volt is defined as the electric potential between two points of a conducting wire when an electric current of one ampere dissipates one watt of power between those points. [2] It can be expressed in terms of SI base units ( m , kg , s , and A ) as
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
These equations taken together are as powerful and complete as Maxwell's equations. Moreover, the problem has been reduced somewhat, as the electric and magnetic fields together had six components to solve for. [1] In the potential formulation, there are only four components: the electric potential and the three components of the vector potential.