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EM problem

  1. Apr 4, 2008 #1
    Consider a wire, if I suddenly pass current on it. There would be an instant localized B field around the wire. Since there is sudden change of B field, there will also be a finite E field. According to Maxwell equation E=B/c.

    As the B field spread out the E field will follow, even when the current is stable and B field stop changing the E field will still be there with the B field. But this has got to be wrong right? Otherwise whenever we turn on a solenoid there will be an observable E field around it!!??
     
  2. jcsd
  3. Apr 4, 2008 #2

    neu

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    The equation you mentioned is not valid.

    I presume you mean:
    [tex]\nabla\times\textbf{E}=-\frac{1}{c}\frac{\partial E}{\partial t}[/tex]

    This Faraday's law:

    from Wikipedia:
    "Faraday's law of induction states that the induced electromotive force in a closed loop of wire is directly proportional to the time rate of change of magnetic flux through the loop."

    So you would get a current in a conductor MOVING through the B-field of a solenoid, but not when static.
     
  4. Apr 4, 2008 #3

    Andy Resnick

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    Neu,

    I think you made an error in the LaTex formula (enroger's is not correct, either). The appropriate equation is:

    [tex]\nabla\times\textbf{H} = \frac{1}{c}( \frac{\partial}{\partial t}\textbf{E}+4\pi \textbf{i})[/tex]

    Differentiating this, to get a time-varying current, and I think you will find that when a solenoid is turned on or off, a pulse of EM radiation is emitted, in accordance with everyday experience. The EEs in the audience should be able to give a better idea of what happens
     
  5. Apr 4, 2008 #4

    neu

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    yeah sorry i meant:
    [tex]\nabla\times\textbf{E}=-\frac{\partial \textbf{B}}{\partial t}[/tex]
     
  6. Apr 4, 2008 #5
    The fact that there is a pulse of E field accompany with B field when the solenoid got turn on has no problem. What I want to know is: When there is no change in current a long time after turn on, therefore no change in B field around the wire, would there still be a E field around the wire?

    I think the answer is no, but I can't derive that out of maxwell equation. help?
     
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