Understanding Gauss's Law for Electric Fields

In summary, Gauss's law states that the net electric flux through a closed surface is equal to the enclosed charge. This means that even though external charges do not contribute to the net flux, they still affect the electric field at a point on the surface. In special cases where there is high symmetry, the electric field can be calculated using the net flux, but in more complex situations, the field must be calculated separately from the net flux.
  • #1
siddharth5129
94
3
My physics textbook emphasizes that the electric field appearing in Gauss's law is the resultant electric field due to charges present both inside and outside the chosen closed surface , while the 'q' appearing in the law is only the charge contained within the surface. .This appears to follow from the mathematical statement of the law as the flux due to externally present charge is ,naturally , zero. But this also seems to suggest that the electric field on the Gaussian surface ( say a sphere ) would be the same whether there is solely one point charge ( which the sphere encloses say ) , or whether there are in addition a collection of point charges present outside the surface. But this cannot be true , can it ? Is there something I missed?
 
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  • #2
siddharth5129 said:
But this also seems to suggest that the electric field on the Gaussian surface ( say a sphere ) would be the same whether there is solely one point charge ( which the sphere encloses say ) , or whether there are in addition a collection of point charges present outside the surface. But this cannot be true , can it ? Is there something I missed?
Even though an external charge doesn't change the net flux through the Gaussian surface, it still affects the field at a point on that surface.
 
  • #3
Doc Al said:
Even though an external charge doesn't change the net flux through the Gaussian surface, it still affects the field at a point on that surface.

So , the electric field that is obtained from Gauss law is not the resultant electric field(due to enclosed charge + external charge) , but is the field due to the enclosed charge only. Am i right ?
 
  • #4
siddharth5129 said:
So , the electric field that is obtained from Gauss law is not the resultant electric field(due to enclosed charge + external charge) , but is the field due to the enclosed charge only. Am i right ?

You do not obtain the electric field from Gauss' Law, you obtain the net electric flux of a closed surface, which, as Doc Al notes, is unaffected by any charges that are not contained in the interior of the closed surface.
 
  • #5
siddharth5129 said:
So , the electric field that is obtained from Gauss law is not the resultant electric field(due to enclosed charge + external charge) , but is the field due to the enclosed charge only. Am i right ?
Gauss's law tells you the net flux through the surface. For certain highly symmetric charge distributions, you can use the net flux to figure out the electric field. In those special situations the electric field you find is the total field due to all charges, but the contribution to the field from external charges will be zero.
 
  • #6
Understood. But what if the external charges modify the field at the Gaussian surface. Doesn't Gauss's law fail to take them into account , simply because they do not contribute to the net flux through the closed surface.
 
  • #7
siddharth5129 said:
Understood. But what if the external charges modify the field at the Gaussian surface. Doesn't Gauss's law fail to take them into account , simply because they do not contribute to the net flux through the closed surface.
If the external charges modify the field at the Gaussian surface, then the situation lacks sufficient symmetry to use the net flux to calculate the field.

Gauss's law always gives you the correct net flux, but only in special cases can it be used to find the field.
 
  • #8
Okay ...I get it now. Thanks
 

1. What is Gauss's law and why is it important in science?

Gauss's law is a fundamental principle in physics that describes the relationship between electric charges and the electric field. It states that the electric flux through any closed surface is equal to the total charge enclosed by that surface divided by the permittivity of free space. This law is important in science because it allows us to calculate the electric field from a known distribution of charges, making it a powerful tool for solving many problems in electromagnetism.

2. How does Gauss's law differ from Coulomb's law?

While both laws deal with the relationship between electric charges and electric fields, they differ in their mathematical expressions and the types of problems they can be used to solve. Coulomb's law deals with the force between two point charges, while Gauss's law deals with the electric field from a continuous distribution of charges, making it more versatile in solving complex problems.

3. Can Gauss's law be applied to any shape or size of charge distribution?

Yes, Gauss's law can be applied to any closed surface and any shape or size of charge distribution, as long as the surface encloses the entire charge. This is one of the advantages of Gauss's law over Coulomb's law, as it allows for easier calculations in more complex situations.

4. What are some real-world applications of Gauss's law?

Gauss's law has many practical applications in science and engineering, such as in the design of electric motors and generators, in the analysis of electromagnetic waves, and in the calculation of the electric field inside a conductor. It is also used in various medical technologies, such as MRI machines, which rely on electromagnetism to produce images of the body.

5. Are there any limitations or exceptions to Gauss's law?

While Gauss's law is a powerful tool, there are some limitations and exceptions to its application. It assumes a vacuum or free space, and may not be accurate in materials with varying permittivity. It also does not take into account the effects of magnetic fields, which may be present in certain situations. Additionally, Gauss's law may not apply to non-steady state situations or in extremely small scales where quantum effects become significant.

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