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Homework Help: Electric field

  1. May 22, 2005 #1
    Given E in a region of space ( [tex]\epsilon_{o} , \mu_{o}[/tex])
    I should think of it as a free space or vacuum?
     
    Last edited: May 22, 2005
  2. jcsd
  3. May 22, 2005 #2
    This is vacuum.
     
  4. May 22, 2005 #3
    I have to find [tex]B[/tex], [tex]\rho[/tex] and [tex]J[/tex]

    [tex] \nabla \times \vec E= -\frac{\partial \vec B}{\partial t} [/tex]

    [tex] \nabla \cdot D=\rho [/tex]

    In free space J = 0 so for J in vacuum I should use

    [tex] \nabla \times H =J+ \frac{\partial D}{\partial t}[/tex]

    or something else?
     
  5. May 23, 2005 #4

    OlderDan

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    You probably want to use

    [tex]D = \epsilon_{o} E [/tex]

    [tex]B = \mu_{o} H, [/tex]

    to eliminate D and H. Don't know if you will need it, but you can round out your set of equations with

    [tex] \nabla \cdot B=0 [/tex]
     
  6. May 23, 2005 #5
    I think I got B, D, H and [tex] \rho[/tex] and using

    [tex] \nabla \times H =J+ \frac{\partial D}{\partial t}[/tex]

    I get J

    What is the difference between free space (J = 0) and vacuum?
     
  7. May 23, 2005 #6

    dextercioby

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    Vacuum means [itex] \mu_{0},\epsilon_{0} [/itex].If you're speaking about "free space",then u should assume no charge density [itex] \rho=0 [/itex] and no charge transport [itex] \vec{J}=0 [/itex].

    So we can have sources in vacuum.But not in free space.

    Free space is typically a vacuum in which electromagetic waves (radiation far away from the sources) propagate.

    Daniel.
     
  8. May 23, 2005 #7
    Thanks, So in my problem I will get J not equal 0
     
  9. May 23, 2005 #8

    dextercioby

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    Please post the text of your problem in its exact form.

    Daniel.
     
  10. May 23, 2005 #9
    In the region of space [tex]\epsilon_{o} , \mu_{o}[/tex]
    [tex]E = (6z\vec{i}+10y\vec{j})cos500t \vec{j}[/tex]

    Find [tex]B, \rho, J[/tex]
     
  11. May 23, 2005 #10

    dextercioby

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    [tex] \nabla\cdot\vec{E}=\frac{\rho}{\epsilon_{0}} [/tex] (1)

    [tex] \nabla\times\vec{E}=-\frac{\partial\vec{B}}{\partial t} [/tex] (2)

    [tex] \nabla\times\vec{B}=\mu_{0}\vec{J}+\mu_{0}\epsilon_{0}\frac{\partial\vec{E}}{\partial t} [/tex] (3)

    Daniel.
     
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