Can Gauss's Law Explain the Field of an Electron in a Closed Finite Universe?

In summary, the conversation discusses Gauss's divergence law and its application in a closed finite universe, specifically in the case of a 4-sphere with a single electron. The conversation also delves into the concept of flux and how it relates to the electric field, as well as potential issues with an infinite range force in a finite space. The possibility of avoiding these issues by stipulating a total charge of 0 in the universe is also mentioned, but the question of how this would affect gravity remains. Finally, there is a discussion about potential confusion between flux and the magnitude of the electric field.
  • #1
Khashishi
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How does Gauss's divergence law work in a closed finite universe? Let's say the universe were a 4-sphere, with a single electron. How can I work out the field of the electron? If I draw a 3-sphere around the electron, then I split space into two regions. One region contains an electron, so Gauss's law tells me that the flux through the sphere is -e*4pi. But the other region doesn't contain any electron, so Gauss's law tells me that the flux through the sphere going the other way is 0. That's inconsistent.

It seems if I think about it a little more, it makes no sense to have an infinite range force in finite space. An electron's field lines would "wrap around" and overlap itself onto infinity.
 
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  • #2
It seems that problems could be avoided by stipulating that the total charge in the universe is 0. But what about gravity then?
 
  • #3
Khashishi said:
It seems that problems could be avoided by stipulating that the total charge in the universe is 0. But what about gravity then?

Well Gauss' law for gravity is Newtonian gravity, which we know is incorrect.
 
  • #4
Why is it inconsistent? Gauss' Law essentially tells you whether or not you have any sources within the volume enclosed by your surface.

For the region without the electron, the flux of electric field through the surface is indeed zero, since any flux entering the volume from outside (where the source is located) is exactly countered by the flux leaving the volume.

For the region with the electron, the only electric fields in the universe (as you defined it) are from the electron, and can only pass outwards through the surface i.e. there is no field coming inwards to counter it, and thus the flux is non-zero.

Are you mixing up flux of the electric field with the actual magnitude of the electric field?

That's not meant to be an insulting question; it's just that I did precisely that when I learned about Gauss' Law. :redface:
 
  • #5
Actually, I think I see where you're coming from now. I'm not sure how to answer that.
 

Related to Can Gauss's Law Explain the Field of an Electron in a Closed Finite Universe?

1. What is Gauss's law in closed space?

Gauss's law in closed space, also known as Gauss's law of electrostatics, is a fundamental law of electromagnetism that relates the electric field at a point to the distribution of electric charges within a closed surface surrounding that point. It states that the net electric flux through any closed surface is equal to the enclosed charge divided by the permittivity of the surrounding medium.

2. How is Gauss's law applied in practical situations?

Gauss's law is commonly used in practical situations to calculate the electric field at a point due to a known charge distribution, such as a point charge, line of charge, or charged surface. It can also be used to determine the total charge enclosed within a closed surface given the electric field at every point on the surface.

3. What is the significance of Gauss's law in closed space?

Gauss's law is significant because it is a fundamental law of electromagnetism that helps us understand and calculate the behavior of electric fields and electric charges. It is also a powerful tool for solving complex problems in electrostatics and is a key concept in the study of electromagnetism.

4. Can Gauss's law be used in non-closed spaces?

Gauss's law is specifically applicable to closed surfaces, as it relies on the concept of a net electric flux through a closed surface. However, there are variations of Gauss's law, such as Gauss's law in differential form, which can be used in non-closed spaces to calculate the electric field at a point due to a charge distribution.

5. Are there any limitations to Gauss's law in closed space?

One limitation of Gauss's law is that it only applies to static electric fields and does not take into account time-varying fields. Additionally, it assumes that the permittivity of the surrounding medium is constant, which may not always be the case in real-world situations. It also does not account for the effects of magnetic fields.

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