Gauss' law for uniformly charged space

• Likith D
In summary, the problem is that Gauss' law disagrees with uniform charged space. It seems to imply that such a charge distribution is not possible, but it may be possible if boundary conditions are met.
Likith D
the problem:
Say we have the entire space uniformly charged. Then, the E field experienced by any point is zero, from symmetry.*
But, it means that for any Gaussian surface, the flux though it is zero even though the charge enclosed is clearly not. Gauss' law seems to disagree with symmetry, but it also cannot 'therefore state' that such a charge distribution is not possible.** (only theoretically, if it should exist)*It is not 'not defined' for the same reasons E field inside a sphere of uniform charge distribution is not 'not defined'... so to say that it is not zero is to go against symmetry of space for that point
**Why would we not have 3d infinite charge distribution while we have 2d infinite charge distribution

attempt at solution:
So, I tried to use the fact that we already computed E field inside a spherical uniformly charged object and let the R tend to infinity which gives ; https://i.stack.imgur.com/N8dwe.jpg independent of radius of sphere.
which may or maynot be zero depending on center of sphere and the point, which makes it weirder... but I have tried integration to find the E field of a uniformly charged wire segment and made it's length tend to infinity to get an answer that agrees with Gauss' law (the same for a planar disc tending to infinite plane, works)... and uniformly charged space seems to be not following that...
Gauss' law just seems to disagree with uniform charged space
what do we make of all this? that Gauss' law is flawed?
If it cannot possibly go against symmetry, does it really imply that uniformly charged space is not possible?

You need boundary conditions, i.e., a behaviour at infinity, that breaks the symmetry in order for Gauss' law to be consistent. This was discussed relatively recently in a featured thread. Boundary conditions that satisfy either translational or rotational invariance will break the other.

Last edited:
Likith D said:
Say we have the entire space uniformly charged. Then, the E field experienced by any point is zero, from symmetry.*
Only at the center of the sphere if the sphere is finite.
If the sphere is not finite see a relatively recent discussion here

1. What is Gauss' law for uniformly charged space?

Gauss' law for uniformly charged space is a fundamental law in electromagnetism that relates the electric field at a point to the charge enclosed by a surface surrounding that point. It states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of the medium.

2. How is Gauss' law used in physics?

Gauss' law is used to calculate the electric field at a point due to a distribution of charges. This law is particularly useful in cases where the distribution of charges has a high degree of symmetry, such as a uniformly charged sphere or a line of charge. It also allows for the calculation of the total charge within a closed surface, even if the distribution of charges is not known.

3. What is the relationship between Gauss' law and Coulomb's law?

Gauss' law is a more general form of Coulomb's law, which describes the electric field generated by a point charge. Gauss' law applies to any distribution of charges, and can be used to calculate the electric field at a point due to multiple charges, while Coulomb's law only applies to a single point charge.

4. How can Gauss' law be used to determine the electric field inside a conductor?

Gauss' law states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of the medium. In the case of a conductor, the electric field inside the conductor must be zero, so the charge enclosed by any closed surface within the conductor must also be zero. This allows for the determination of the electric field inside the conductor.

5. What are the limitations of Gauss' law?

Gauss' law is only applicable to static electric fields and cannot be used to calculate the electric field in situations where charges are moving or changing over time. It also assumes that the medium in which the charges are located is linear and isotropic, meaning that the electric field is directly proportional to the charge and is the same in all directions. This may not be the case in all situations, so care must be taken when applying Gauss' law.

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