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