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Why a magnetic flux in closed surface area is always 0?

  1. Jan 17, 2008 #1
    Why a magnetic flux in closed surface area is always 0?
     
  2. jcsd
  3. Jan 17, 2008 #2

    dst

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    Apply Lenz' law to a spherical hollow surface, all the charges move to oppose the magnetic field and each other and it all cancels out.

    Compare with gravity...
     
  4. Jan 17, 2008 #3
    Do you have some diagram or picture?
     
  5. Jan 17, 2008 #4
    Hmmm dst, can you explain this further? This is very similar to how the Faraday's cage works right?
     
  6. Jan 17, 2008 #5
    the E field entering the close surface is equal to the E field exiting the close surface ;)


    oops, it should be magnetic flux instead of e field
     
    Last edited: Jan 17, 2008
  7. Jan 17, 2008 #6

    Doc Al

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    Staff: Mentor

    Gauss' Law for Magnetism

    This is one of Maxwell's equations. It essentially says that there are no magnetic monopoles (only dipoles, which give no net flux through any surface surrounding them). See: Gauss' Law for Magnetism

    Contrast this with Gauss's law for electric fields. No problem getting a non-zero electric flux through a closed surface--just have it enclose a net charge.
     
  8. Jan 17, 2008 #7
    I saw that law, but still can't understand what is happening inside the closed surface.
     
  9. Jan 17, 2008 #8
    0 magnetic flux, is 0 times the magnetic field is perpendicular to the area or what? As I know Gauss' law for Magnetism is different for electric fields. In case of electric fields, it is not zero.
     
    Last edited: Jan 17, 2008
  10. Jan 17, 2008 #9

    Doc Al

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    The net magnetic flux through a closed surface is zero. Magnetic flux is defined and illustrated here: Magnetic Flux
     
  11. Jan 17, 2008 #10
    In the case of STATIONARY fields, the magnetic flux through a closed surface is definitely zero.
    And what about non-stationary fields? Is it still zeroing?

    PS
    I am so lazy to take integral... maybe anybody already knows the answer? :confused:
     
  12. Jan 17, 2008 #11

    Doc Al

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    Yep. Maxwell's equations still hold.
     
  13. Jan 17, 2008 #12
    Does it help to think about the fact that lines of magnetic flux are always closed loops (since there are no monopoles for them to begin or end on)? You can't draw a closed loop that intersects a closed surface at only one point; it goes in at one point and out at another - i.e. number of "innies" = number of "outies", hence zero net flux.
     
  14. Jan 17, 2008 #13
    Does it have something with the Faraday's cage?
     
  15. Jan 17, 2008 #14
    Not really - as stated in a previous post, the lines of electric flux do not have to total zero through a closed surface. The Faraday cage has more to do with charges in the cage realigning themselves to cancel the contained field. It works only with an electrically conductive closed surface; it's not true for just any mathematical closed surface, as it is for the case of the magnetic flux through a closed surface.
     
  16. Jan 17, 2008 #15
    But isn't the magnetic flux, a magnetic field perpendicular to some area? How is possible that the magnetic field is 0, when still it exists?
     
  17. Jan 17, 2008 #16
    You can define a surface perpendicular to the lines of the magnetic field if you want to, but that's not necessary for the statement in question - it's true for any closed surface, no matter how it is oriented.

    And no - the magnetic field is not zero, nor is the flux (this was stated in an earlier post - please read them all). It's the net flux, i.e. the sum of all the flux lines across the surface, that is zero. It just means that there is much field "flowing" out of the surface as there is field "flowing" into the surface. Again, it has to do with the closed loops: every one that exits must also reenter.
     
  18. Jan 17, 2008 #17
    Ok, I understand now. And what happens in the Faraday's cage? Are just the sum of all the flux lines zero?
     
  19. Jan 17, 2008 #18
    Well, that's kind of a funny question, since a Faraday cage relies on the presence of electric charges on the surface, so there will be flux line originating on the surface itself. I guess the correct thing to say, since there are no flux lines in the space inside the surface, is that the flux lines from any external field are exactly cancelled by the flux lines from the rearranged charges on the cage, so you could conclude that the flux is zero everywhere on the surface, not just summed up.

    That's my immediate response, anyway. Maybe someone else will disagree ... :confused:
     
  20. Jan 17, 2008 #19
    And can I ask you another question? How is possible that the field of the permanent magnet is changed (delta B)? Here is the link.
     
  21. Jan 17, 2008 #20

    Doc Al

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    Staff: Mentor

    The field of the permanent magnet is not being changed. The field (and thus flux) within the conducting loop changes as the magnet is moved.
     
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