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{{r|Vector field}}

Because an electric field '''E''' is a [[vector field]], it is defined at every point '''r''' of space. Usually the space consid Because of the [[Helmholtz decomposition]] of a general vector field, we can write

{{r|Vector field}}

{{r|Vector field}}

...oth sides of the equation and using that the divergence of the curl of any vector field is zero (i.e. <math> \boldsymbol{\nabla} \cdot \boldsymbol{\nabla} \times \

...'' (also known as '''rotation''') is a differential operator acting on a [[vector field]]. It is defined in the branch of mathematics known as [[vector analysis]]. where '''F''' is a vector field.

{{r|Vector field}}

...(also known as vacuum permeability), and ''c'' is the speed of light. The vector field '''B''' is known as the [[magnetic induction]]. The direction of integratio ...ptstyle \boldsymbol{\nabla}\times \mathbf{B}</math> is the [[curl]] of the vector field '''B'''('''r''') and '''J'''('''r''') is the current density (amount of cha

As any [[vector field]], the [[electric field]] '''E''' appearing in the Lorentz force '''F'''

Hence, F is a vector field of finite dimension over <math>\mathbb{F}_p</math>. Moreover since the non

...-align: top"><math> \mathbb{R}^3</math></font> is the decomposition of the vector field into two vector fields, one a [[divergence]]-free field and one a [[curl]]- Any vector field '''F'''('''r''') that is sufficiently often differentiable and vanishes suf

{{r|Vector field}}

{{r|Vector field}}

...agnetic field lines are shown in blue. The magnetic induction '''B''' is a vector field tangent to field lines. The direction of '''B''' and ''i'' are connected vi

{{r|Vector field}}

...describes a magnetic field (a vector) at every point in space; it is a [[vector field]]. In non-relativistic physics, the space in question is the three-dimensi ...d '''H''' is closely related to the [[magnetic induction]] '''B''' (also a vector field). It is the vector '''B''' that enters the expression for magnetic force on

...sm)|"free" space]]), both '''E''' and '''B''' can be derived from a third vector field, the [[vector potential]] '''A'''. Below, the [[Fourier transform]] of the ==Fourier expansion of a vector field==

...tric displacement''' and usually denoted by its first letter '''D''', is a vector field in a non-conducting medium, a [[dielectric]]. The displacement '''D''' is p The vector field '''P''' describes the polarization (small separation of the charges on eac

{{r|Vector field}}

...0''' somewhere within &rho;. The electric field '''F''' is a homogeneous [[vector field]]. With ''V''('''0''') as the zero of potential, the interaction becomes