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Positive source for electromagnetic energy

  1. Jul 24, 2013 #1

    ShayanJ

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    We know that the conservation of electromagnetic energy is expressed via the continuity equation below:
    [itex]
    \large{\frac{\partial u}{\partial t}}+\vec{\nabla}\cdot\vec{S}=-\vec{J}\cdot\vec{E}
    [/itex]
    with [itex] u=\frac{1}{2}(\vec{E}\cdot\vec{D}+\vec{B}\cdot\vec{H}) [/itex] and [itex] \vec{S}=\vec{E}\times\vec{H} [/itex].
    It is obvious that the term [itex] -\vec{J}\cdot\vec{E} [/itex] is a source for electromagnetic energy and we know that its usually negative and electromagnetic energy is dissipated(through joule heating).
    My question is,is there a physical situation in which [itex] -\vec{J}\cdot\vec{E} [/itex] becomes positive and,somehow,energy is added to the field?
    Thanks
     
  2. jcsd
  3. Jul 24, 2013 #2
    Sure. Consider a fast-moving charged particle being slowed by an electric field. The charged particle loses kinetic energy and the electromagnetic field gains energy. Often we think of the particle as gaining electric potential energy, but really this potential energy is the energy of the electric field.
     
  4. Jul 24, 2013 #3

    ShayanJ

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    Gold Member

    Oohh...of course!
    You know...I was just looking for a special combination of current density and electric field and didn't remember this really trivial case!
    But...how would you write [itex] \vec{J} \cdot \vec{E} [/itex] for this case?
    Thanks
     
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