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field (physics)
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Definition/Summary
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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]). |
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Equations
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Lorentz force (for electromagnetic field):
[tex]\mathbf{F}\ =\ q(\mathbf{E}\ +\ \mathbf{v}\times\mathbf{B})[/tex] |
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Recent forum threads on field (physics)
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Breakdown
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Physics
> Electromagnetism
>> Electromagnetic Waves
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Extended explanation
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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. |
Commentary
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