Gauss’s law of electrostatic and Continuous charge distribution

 

Continuous charge distribution

1)It means the distribution of charges, it does not mean single charges like q_1, q_2, q_3,  q_{4, ..…………..} q_n.

2)Charges may be distributed in surface, in a line or in a volume.

3)Surface charge density denoted as σ is ----->

 

4)linear charge density denoted as λ is defined as ----->

5)volume charge density denoted as ρ is defined as  ----->

 

Gauss’s law of electrostatic

Gauss’s law of electrostatic state that total electric flux in a closed surface is equal to the total charge inside the closed surface divided by the permittivity. That is

 

Derivation or proof of Gauss’s law

1)We know electric flux is equal to the product of the electric field E and the perpendicular surface area  That is

2)For a point charge q, the electric field at a distance r is

Now draw a closed sphere of r as radius around the charge q taking as centre.

Now the total area of the sphere is 

Therefore the electric flux  is

Hence proved.