Surface Integrals in Gauss's Theorem of Charge in Motion

In summary: It's usually best to choose a surface that is stationary in whatever reference frame you're working in.In summary, Gauss's theorem can be applied to charge in motion and the surface integral can be taken over any chosen Gaussian surface. The value used for charge should be the charge inside the surface at the time of calculation, assuming no charges with relativistic speed are present. Maxwell's equations are fully relativistic and it may be necessary to consider a time-average in some cases. It is important to choose a stationary surface when the Gaussian surface is also moving.
  • #1
BIT1749
13
0
gauss's theorem is also applicable to charge in motion.but how the surface integral has to be taken??
 
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  • #2
However you like. You can choose any gaussian surface, it does not need to follow the charge in any way.
 
  • #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??
 
  • #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)
 
  • #5
What book was this? Gauss' law is true instantaneously.
 
  • #6
BIT1749 said:
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.

BIT1749 said:
.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.
 
  • #7
dauto said:
(assuming no charges with relativistic speed are present)
I don't think that is a necessary assumption. Maxwell's equations are fully relativistic already.
 
  • #8
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??
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.
 

Related to Surface Integrals in Gauss's Theorem of Charge in Motion

1. What is a surface integral in Gauss's Theorem of Charge in Motion?

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.

2. How is a surface integral related to Gauss's Theorem of Charge in Motion?

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.

3. What is the significance of Gauss's Theorem of Charge in Motion?

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.

4. Can surface integrals in Gauss's Theorem of Charge in Motion be used for both stationary and moving charges?

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.

5. How can surface integrals in Gauss's Theorem of Charge in Motion be applied in real-world situations?

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.

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