Gauss's Law Problem: General than Coulomb's Law?

In summary, Gauss's law is a more general law than Coulomb's law, as it can be applied to moving charges with varying velocities and accelerations. However, when dealing specifically with moving charges, Coulomb's law cannot be used and the Lienard-Wiechert potentials must be used instead. While Gauss's law still applies in these cases, it can only be used to find the integral of E over a closed surface and not the specific value of E at a given point. This is due to the loss of symmetry caused by the movement of charges, which also affects the magnetic flux. The failure of Coulomb's law in this scenario is demonstrated by the non-zero curl of E, indicating changes in the magnetic field over
  • #1
Kolahal Bhattacharya
135
1
I read in Corson and Lorrain that Gauss's law is more gneral than Coulomb's law.It can even be applied to moving charges whatever be their velocities/accelerations.Can anyone explain this?
 
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  • #2
Coulomb's law cannot be applied to moving charges.
The Lienard-Wiechert potentials have to be used.
Since div E=4pi rho in all cases, Gauss's law still applies.
However since the symmetry is lost, Gauss's law just gives the integral of E over a closed surface and can't be used to find E(r).
 
  • #3
Well,I found it in a text I mentioned.I think we may think this way:the charge inside the closed surface will be static or moving.Whatever the case,the fluxes are electric as well as magnetic.Gauss's law still holds because, magnetic flux out of a closed surface is zero.We do not find the B field when charges inside are in motion.
 
  • #4
This is clear if we look at the Maxwell Equations. The curl of E is no longer zero, for the particle is moving and that makes the B changing with time. Thus the Coloumb's Law fails but div E is unchanging and Gauss's Law holds.
 

Related to Gauss's Law Problem: General than Coulomb's Law?

1. What is Gauss's Law Problem?

Gauss's Law is a fundamental law in electromagnetism that describes the relationship between electric charges and electric fields. It states that the electric flux through a closed surface is proportional to the charge enclosed by that surface.

2. How is Gauss's Law different from Coulomb's Law?

Coulomb's Law states that the force between two electric charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Gauss's Law is a more general formulation that takes into account the distribution of electric charges in a given space.

3. What are some real-life applications of Gauss's Law?

Gauss's Law has many practical applications, such as determining the electric field inside a charged conductor, calculating the electric field of a charged sphere, and understanding the behavior of electric charges in capacitors and other electrical circuits.

4. How do you solve a Gauss's Law problem?

To solve a Gauss's Law problem, you first need to understand the given scenario and identify the relevant parameters, such as the enclosed charge, the surface area, and the electric field. Then, you can use the mathematical formula of Gauss's Law to calculate the electric flux and solve for the unknown variables.

5. Are there any limitations to Gauss's Law?

Like any other scientific law, Gauss's Law has its limitations. It only applies to static electric fields and does not account for changing magnetic fields. Additionally, it assumes a vacuum or uniform medium, so it may not accurately describe electric fields in more complex environments.

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