Gauss' Law: Discrete vs Continuous Charges

[physicsprasanna]

why is it that a gaussian surface cannot pass through discrete charges ... but can pass through a continuous charge distribution??

 

[Astronuc]

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

 

[physicsprasanna]

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?

 

[BananaMan]

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

 

[lifesfun]

may i know what is distribution charge?

 

[Galileo]

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.

 

[physicsprasanna]

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!

 

[Astronuc]

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