Electric field

  • Thread starter robert25pl
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  • #1
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Given E in a region of space ( [tex]\epsilon_{o} , \mu_{o}[/tex])
I should think of it as a free space or vacuum?
 
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  • #2
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This is vacuum.
 
  • #3
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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?
 
  • #4
OlderDan
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robert25pl said:
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?

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]
 
  • #5
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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?
 
  • #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.
 
  • #7
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Thanks, So in my problem I will get J not equal 0
 
  • #8
dextercioby
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Please post the text of your problem in its exact form.

Daniel.
 
  • #9
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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]
 
  • #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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