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What is a field (physics)

  1. Jul 24, 2014 #1
    Definition/Summary

    A field is a map that attaches a (scalar, vector, tensor, etc.) value to every element of an underlying space.

    For example, the electric field [itex]\mathbf{E}[/itex] and the magnetic field [itex]\mathbf{B}[/itex] are vector fields over three-dimensional space, while the electromagnetic field is the Faraday tensor field [itex](\mathbf{E};\mathbf{B})[/itex] over four-dimensional space-time.

    A field may be a force, the potential of a force, or something ordinary such as temperature.

    The force exerted by a force field on a body depends on the strength of the field, and on various characteristic of the body (including mass, velocity, spin, and various types of charge).

    The units in which a force field is measured depend on those characteristics (so, for example, the units of [itex]\mathbf{E}[/itex] have dimensions of velocity times the units of [itex]\mathbf{B}[/itex]).

    Equations

    Lorentz force (for electromagnetic field):

    [tex]\mathbf{F}\ =\ q(\mathbf{E}\ +\ \mathbf{v}\times\mathbf{B})[/tex]

    Extended explanation

    Flux:

    The flux of a field through a surface is the total component of its strength perpendicular to that surface.

    Conservative vector field:

    A vector field is conservative if it is the gradient of a (non-unique) scalar field (the potential):

    [tex]\mathbf{V}\ =\ \nabla\,\phi[/tex]

    So the curl of a conservative vector field is zero (the field is irrotational):

    [tex]\nabla\ \times\ \mathbf{V}\ =\ \nabla\ \times\ \nabla\,\phi\ =\ 0[/tex]

    Solenoidal vector field:

    A vector field is solenoidal if it is the curl of a (non-unique) vector field (the vector potential):

    [tex]\mathbf{V}\ =\ \nabla\,\times\mathbf{A}[/tex]

    So the divergence of a solenoidal vector field is zero:

    [tex]\nabla\cdot\mathbf{V}\ =\ \nabla\ \cdot\ \nabla\,\times\mathbf{A}\ =\ 0[/tex]

    Any vector field may be expressed as the sum of a conservative vector field and a solenoidal vector field.​

    * This entry is from our old Library feature. If you know who wrote it, please let us know so we can attribute a writer. Thanks!
     
  2. jcsd
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