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## Main Question or Discussion Point

gauss's theorem is also applicable to charge in motion.but how the surface integral has to be taken??

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gauss's theorem is also applicable to charge in motion.but how the surface integral has to be taken??

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Dale

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What book was this? Gauss' law is true instantaneously.

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Dale

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No, the integral is a 2D integral over a spatial surface defined at a single instant of time.i have read in a book that the surface integral has to be taken over a period of time

huh? You put the charge in place of the charge. You can't put anything else there..but what value should we put in place of charge??

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Dale

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I don't think that is a necessary assumption. Maxwell's equations are fully relativistic already.(assuming no charges with relativistic speed are present)

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BruceW

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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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