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Gauss's Theorem

  1. Sep 16, 2013 #1
    gauss's theorem is also applicable to charge in motion.but how the surface integral has to be taken??
     
  2. jcsd
  3. Sep 16, 2013 #2

    Dale

    Staff: Mentor

    However you like. You can choose any gaussian surface, it does not need to follow the charge in any way.
     
  4. Sep 17, 2013 #3
    i have read in a book that the surface integral has to be taken over a period of time.but what value should we put in place of charge??
     
  5. Sep 17, 2013 #4
    you use the charge that was inside of the surface at the moment you chose to do the calculation (assuming no charges with relativistic speed are present)
     
  6. Sep 17, 2013 #5
    What book was this? Gauss' law is true instantaneously.
     
  7. Sep 17, 2013 #6

    Dale

    Staff: Mentor

    No, the integral is a 2D integral over a spatial surface defined at a single instant of time.

    huh? You put the charge in place of the charge. You can't put anything else there.
     
  8. Sep 17, 2013 #7

    Dale

    Staff: Mentor

    I don't think that is a necessary assumption. Maxwell's equations are fully relativistic already.
     
  9. Sep 18, 2013 #8

    BruceW

    User Avatar
    Homework Helper

    In that specific example, they may have been considering a time-average... But in general as others have said, Gauss' theorem works at every instant of time. So you can integrate over time and then divide by the time interval if you want to get a time average.

    edit: p.s. be careful in cases where the Gaussian surface is also moving.
     
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