Gauss' Law: Discrete vs Continuous Charges

In summary, Gaussian surfaces cannot pass through discrete charges, but can pass through a continuous charge distribution. This is due to the singularity that Gauss's Law encounters when passing through a point charge.
  • #1
physicsprasanna
20
0
why is it that a gaussian surface cannot pass through discrete charges ... but can pass through a continuous charge distribution??
 
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  • #2
I believe technically, the Gaussian surface must enclose the charges, because Gauss's law applies to the enclosed charge.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html#c2

The electric flux through an area is defined as the electric field multiplied by the area of the surface projected in a plane perpendicular to the field. Gauss's Law is a general law applying to any closed surface. It is an important tool since it permits the assessment of the amount of enclosed charge by mapping the field on a surface outside the charge distribution. For geometries of sufficient symmetry, it simplifies the calculation of the electric field.
Hyperphysics

For Gaussian surfaces -
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gausur.html#c1

One can put a Gassian surface just outside a distributed charge.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gausur.html#c3
 
  • #3
i mean ... yes, the gaussian surface should enclose charges .. but the surface should not pass through a discrete charge... but it can pass through a continuous charge distribution ... why is that?
 
  • #4
id assume its fairly hard for it to pass through a point charge as you take the "size" of the charge to be 0 and therefore it cannot have anything pass through it, a continuous charge distribution however has a size and then the surface can pass through it
 
  • #5
may i know what is distribution charge?
 
  • #6
The electric field of a continuous charge distribution is everywhere defined, while the field of a point charge doesn't exist right at the location of the point charge. I believe that singularity is what invalidates the use of Gauss' law when the surface passes through it.
 
  • #7
thanks for the replies ... maybe it is due to the fact that the field due to a charge does not exist at the place of the charge.

Thanks once again!
 
  • #8
lifesfun said:
may i know what is distribution charge?
Simply a collection of charges, but mathematically we treat them as 'uniformly' distributed rather than discrete units.

In a line conductor, the charge is 'linear charge density' or charge/unit length (e.g. C/m).

On a surface conductor, one takes of charge/unit surface (e.g. C/m2) area as though the charges were 'smeared' on the surface. In a conductor, the net charge occurs near the surface because this represents least energy, and the charge units (electrons) are mobile.

In a dielectric, the charges are much less mobile and one can have a volumetric distribution (even non-uniform) of charge.

See - http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html#c1

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html#c4
 

1. What is Gauss' Law?

Gauss' Law is a fundamental law in physics that relates the electric field to the distribution of electric charges. It states that the electric flux through a closed surface is equal to the total charge enclosed by that surface divided by the permittivity of free space.

2. What is the difference between discrete and continuous charges?

Discrete charges refer to individual point charges, while continuous charges refer to a distribution of charges over a continuous region. Discrete charges can be represented as distinct points, while continuous charges require integration to calculate the total charge.

3. How does Gauss' Law apply to discrete charges?

For discrete charges, Gauss' Law states that the total electric flux through a closed surface is equal to the sum of the individual point charges enclosed by that surface divided by the permittivity of free space.

4. How does Gauss' Law apply to continuous charges?

For continuous charges, Gauss' Law states that the total electric flux through a closed surface is equal to the integral of the electric field over that surface, multiplied by the permittivity of free space.

5. Which type of charge distribution is easier to calculate using Gauss' Law?

Continuous charge distributions are generally easier to calculate using Gauss' Law because they can be represented by a continuous function and can be solved using integration. Discrete charge distributions may require more complex calculations due to the need to account for individual point charges.

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