Continuous Charge Distribution

In continuous charge distribution, the charge is uniformly distributed over the conductor. In continuous charge distribution, individually charged particles bound to each other are separated by regions containing no charge. When the charge is continuously flowing over a surface or volume, that distribution is called the surface continuous charge distribution.

Charge density represents how close they are to each other at a specific point. Another definition of continuous charge distribution is that an infinite number of charges are bound to each other and have little space between them, but it doesn’t mean it is not uninterrupted.

In other words, in continuous charge distribution, all charges are tightly bound and have less space between them.

Uniform Charge Distribution: if the charge is distributed uniformly but is not concentrated in any section is described as Uniform Charge Distribution.

Non-Uniform Charge Distribution: if the charge is not distributed uniformly and is not spread over the surface uniformly, it is described as Non-Uniform Charge Distribution.

Types of Continuous Charge Distribution

There are three types of continuous charge distribution which are as follows:

1. Linear Charge: linear charge density
2. Surface Charge: surface charge density
3. Volume charge: volume charge density

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

λ= q/l

dq = λ.dl

The linear load of the density unit is C/m; 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.

dq=λ dl

Surface charge density: Surface charge density is defined as a charge per area of the unit. It is denoted with the symbol sigma.

It is also denoted symbol sigma and unit C/m2. It is also defined as a charge /per area of the unit.

σ = dq/ ds

Where dq is a minor element of charge over a small surface so there will be a small charge on the driver

dq= σ ds

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. It is volume charge distribution. It is denoted (rho) ⍴ symbol.

The charge per unit volume is called volume charge density, and the unit is C/m3, and the density of volume charge is ⍴ = dq/dv

Where dq is a minor charge element located in small volume dv

dq = ⍴dv

Some Examples of Line, Surface, and Volume Charges

Whenever two charged circles are associated by directing wire, charge thickness will become uniform throughout the surface area of the two circles.

Problem: The electric field is given as E = k Q/r2 where k and Q are the charges of the circle, and r is the sweep of the circle. Here charge is equal to the charge of an electron and the radius is r = 10-10 m. Find the value of the electric field.

Solution:

According to the problem statement,

k = 9 ×10⁹

Q = 1.602 x 10^-19 C

And r = 10^-10 m

The electric will be,

E = 9 ×10⁹ x(1.602×10^-19 )/(10^-10)² = 14.418 x 10¹⁰ N/C

From electrostatics, volume charge dispersion is when the charge is consistently distributed over the volume.

Electric Field due to a Continuous Charge of Distribution

The charge dispersion is continuous rather than discrete. It divides the charges into tiny 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.

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