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BIT1749
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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.BIT1749 said: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.BIT1749 said:.but what value should we put in place of charge??
I don't think that is a necessary assumption. Maxwell's equations are fully relativistic already.dauto said:(assuming no charges with relativistic speed are present)
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.BIT1749 said: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??
A surface integral in Gauss's Theorem of Charge in Motion is a mathematical calculation that allows us to determine the total charge passing through a closed surface. It takes into account both the direction and magnitude of the electric field at every point on the surface.
The surface integral is an essential part of Gauss's Theorem of Charge in Motion. It is used to calculate the flux of the electric field through a closed surface, which is an integral part of the theorem's equation.
Gauss's Theorem of Charge in Motion is a fundamental law in electromagnetism that relates the electric field to the distribution of electric charge. It allows us to calculate the electric field at any point in space using the charge distribution, making it a crucial tool in many practical applications.
Yes, surface integrals in Gauss's Theorem of Charge in Motion can be used to calculate the electric field for both stationary and moving charges. However, the calculation may be more complex for moving charges as it involves considering the changing electric field at different points on the surface.
Surface integrals in Gauss's Theorem of Charge in Motion have various practical applications, such as in calculating the electric field around charged objects or in analyzing the behavior of electric fields in different materials. It is also used in the study of electromagnetic waves and in designing electrical circuits.