Continuous Charge Distribution

In continuous charge distribution, the charge is uniformly distributed over the conductor. Individual charges are much closer to each other because they have less space between them. When the charge is continuously flowing over a surface or volume, that distribution is called the continuous charge distribution. Charge density represents how close the charges are to each other at a specific point.

Non-uniform charge distribution: If the charge is not distributed uniformly and does not dissipate over the surface uniformly, it is described as non-uniform charge distribution.

Uniform charge distribution: If the charge is distributed uniformly and is not concentrated in any section is described as uniform charge distribution.

Types of continuous charge distribution

There are three types of continuous charge distribution:

1. Linear charge density 

Linear charge density is defined as electric charge per unit length and is denoted by lambda ().

= dqdl

dq = . dl

The unit of a linear load of density isCm. If we find a conductor with a length of l with a surface load density and take an aspect of dl on it, then a small charge will be on it. Such that-

q= ∫dl

2. Surface charge density

Surface charge density is defined as a charge per area of the unit. It is denoted with the symbol sigma (). Its unit is- C/m2. 

= Qs

Where,

Q is a minor element of charge over a small surface.

s is a charged sheet’s small area.

The charge is represented as-

q = ds

and 

q = ∫ ds

3. Volume charge density

The charge per unit volume is called volume charge density. Its unit is C/m3 and is denoted by the (rho) symbol. Volume charge density is represented as-

  = QV.

 Where Q is a minor charge element located in a small volume.

V is a volume of a charged sphere on a macroscopic scale.

Unit of is C/m3

dq= dv

q = ∫ dv

Continuous charge of distribution due to the electric field 

The charge dispersion is continuous rather than discrete. We can say that it divides the charges into infinitesimal pieces and treats each piece as a point charge, but because the charge is quantised, there is no such thing as truly continuous charge distribution. The electric field for the continuous charge distribution can be determined using the superposition principle and Coulomb’s law. We can determine any charge distribution for continuous or discrete or part continuous or part discrete using these laws.

Electric field due to continuous charge distribution for 1 and n volume charge distribution can be calculated by Coulomb’s law, and the superposition principles are as follows:

1. Due to linear charge distribution:

dF = 140 lr2r

Hence, F = q040 lr2r

q0 is referred to point charge at point p

r is referred to as distance from Δl 

2. Due to surface charge distribution: 

dF = q040 Sr2r

Hence, F = q040 Sr2r

q0 is point charge at point p

r is referred to as distance from Δs 

3. Due to volume charge distribution: 

dF = q040 pVr2r

Hence, F = q040 pVr2r

q0 is referred to point charge at point p

r is referred to as distance from Δv

Conclusion

In the continuous charge distribution system, the charge is uniformly distributed over the conductor. Three types of charge distribution are linear charge, surface charge and volume charge. Due to continuous charge distribution in the electric field, the charge dispersion is continuous. Electric field for continuous charge distribution can be obtained by the superposition principle and Coulomb’s law.