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field (physics)

 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 $\mathbf{E}$ and the magnetic field $\mathbf{B}$ are vector fields over three-dimensional space, while the electromagnetic field is the Faraday tensor field $(\mathbf{E};\mathbf{B})$ 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 $\mathbf{E}$ have dimensions of velocity times the units of $\mathbf{B}$).

 Equations Lorentz force (for electromagnetic field): $$\mathbf{F}\ =\ q(\mathbf{E}\ +\ \mathbf{v}\times\mathbf{B})$$

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 Recent forum threads on field (physics)

 Breakdown Physics > Electromagnetism >> Electromagnetic Waves

 See Also electric displacement felectric fieldMaxwell's equations

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 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): $$\mathbf{V}\ =\ \nabla\,\phi$$ So the curl of a conservative vector field is zero (the field is irrotational): $$\nabla\ \times\ \mathbf{V}\ =\ \nabla\ \times\ \nabla\,\phi\ =\ 0$$ Solenoidal vector field: A vector field is solenoidal if it is the curl of a (non-unique) vector field (the vector potential): $$\mathbf{V}\ =\ \nabla\,\times\mathbf{A}$$ So the divergence of a solenoidal vector field is zero: $$\nabla\cdot\mathbf{V}\ =\ \nabla\ \cdot\ \nabla\,\times\mathbf{A}\ =\ 0$$ Any vector field may be expressed as the sum of a conservative vector field and a solenoidal vector field.

Commentary

 nim2010 @ 07:54 PM Jun21-10 thank u for u r help. If possible please add some more information about modified wave equqtion for electric & magnetic fields in conductors

 born2bstar @ 01:44 AM Jun7-10 yea.......but how could that work?

 tasnim rahman @ 12:57 PM Apr17-10 would someone define the electric field for an oscillating charge, far away from the charge? see at: www.colorado.edu/physics/2000/waves_particles/wpwaves5.html

 tiny-tim @ 04:02 AM Sep27-08 didn't change anything … just fixed the LaTeX

 Gokul43201 @ 11:39 PM Aug7-08 Modified definition

 tiny-tim @ 05:55 AM Jul24-08 Would someone else like to add gauge fields, electroweak field, etc?