Introduction to Gauss Law: It is basically one of the field theories.
Gauss Law is one of the elementary laws of electromagnetism which come from experiential observation and attempts to match experiments with some kind of self- consistent mathematical framework.
It (Gauss Law) states that:
Where (D) is the electric displacement vector, that is interrelated to the electric field vector, (E), by the relationship (D = εE.) where " ε" is called the dielectric constant. NOTE: "D" must have units of "Coulomb / cm2 so that everything works fine) Qencl is the total amount of charge enclosed in the volume "V", which is obtained by doing a volume integral of the charge density "ρ(v)".
Integral form of Gauss' Law
1st Equation(also known as integral form of Gauss' Law) says that if you add up the surface integral of the displacement vector "D" over a closed surface "S ", what you get is the sum of the total charge enclosed by that surface.
We will now convert this equation to its differential form. This will be done by first shrinking down the volume "V" until we can treat the charge density "ρ(v)" as a constant ρ, and replace the volume integral with a simple product.
Hence Gauss' Law would be:
∮DdS = ε∮EdS
= ρΔV
Gauss Law is one of the elementary laws of electromagnetism which come from experiential observation and attempts to match experiments with some kind of self- consistent mathematical framework.
It (Gauss Law) states that:
Where (D) is the electric displacement vector, that is interrelated to the electric field vector, (E), by the relationship (D = εE.) where " ε" is called the dielectric constant. NOTE: "D" must have units of "Coulomb / cm2 so that everything works fine) Qencl is the total amount of charge enclosed in the volume "V", which is obtained by doing a volume integral of the charge density "ρ(v)".
Integral form of Gauss' Law
1st Equation(also known as integral form of Gauss' Law) says that if you add up the surface integral of the displacement vector "D" over a closed surface "S ", what you get is the sum of the total charge enclosed by that surface.
We will now convert this equation to its differential form. This will be done by first shrinking down the volume "V" until we can treat the charge density "ρ(v)" as a constant ρ, and replace the volume integral with a simple product.
Hence Gauss' Law would be:
∮DdS = ε∮EdS
= ρΔV
