Surface Integrals in Gauss's Theorem of Charge in Motion

[BIT1749]

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

 

[Dale]

However you like. You can choose any gaussian surface, it does not need to follow the charge in any way.

 

[BIT1749]

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??

 

[dauto]

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)

 

[mikeph]

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

 

[Dale]

i have read in a book that the surface integral has to be taken over a period of time

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

.but what value should we put in place of charge??

huh? You put the charge in place of the charge. You can't put anything else there.

 

[Dale]

(assuming no charges with relativistic speed are present)

I don't think that is a necessary assumption. Maxwell's equations are fully relativistic already.

 

[BruceW]

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??

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.