We know that the smallest form of charge we can obtain would be positive or negative means the charge of an electron or a proton hence charges are quantized.
The meaning of Continuous charge distribution are that all charges are closely bound together and having very less space between them.
Continuous Charge Distribution
When the charge is uniformly distributed over a conductor it is called as a continuous charge distribution. In a continuous charge distribution, the infinite number of charges are packed closely with each other so that there is no space left between them.
Charge Density
Charge density is defined as the measure of charge per unit area of a surface or per unit volume of a body. Charge density can be calculated in terms of volume, area, or length.
Type of Continuous Charge Distribution
Three types of continuous charge distribution are given below-
1. Linear charge distribution
2. Surface charge distribution
3. Volume charge distribution
Linear charge distribution
The charge distributed over a conductor length is called as the linear charge distribution.
It is denoted by the symbol λ (lambda).
In mathematically
The linear charge distribution dq over the length dl can be written as
λ = dq / dl
Unit of linear charge distribution – coulomb per meter.
Charge dq is found over a small length dl.
If we calculate the big amount of charge over the complete length L then it is given as-
dq = λ dl
Also, electric field dE is given by,
dE = k dq / r2
Putting dq from above equation we get
dE = k λ dl / r2
By integration
dE = k λ dl / r2
For getting the electric field in charge distribution
dE = k/r2 λ dl
Surface charge distribution
If the charge is uniformly distributed over a surface then it is called continuous surface charge distribution.
It is also called as charge per unit area and it is denoted by (sigma).
Units of surface charge density – coulombs per square meter.
Mathematically, surface charge density is given as-
= dq /ds
Electric field create by a small charge dq is written by dE and it is shown as-
dE = k dq / r2
Putting the value of dq, we have,
dE = k ds / r2
To find the complete electric field E over the surface which is produced by charge Q is –
By integration
dE = k ds / r2 = dE = k/r2 ds
Volume charge distribution
When the charge is uniformly distributed over a space or volume of any metal it is known as volume charge distribution or volume charge density or charge per unit volume.
It is represented by the symbol ρ (rho) and is denoted by coulomb per cube meter (C/m3).
Mathematically,
volume charge distribution is given by-
ρ = dq / dv
Here,
dq = small charge found over a small volume.
When these charge are move a small amount of electric field will also be generated.
This electric field is shown by dE which is given as-
dE = k dq / r2
By putting the value of dq from the above equation we get –
dE = k ρ dv / r2
By integration
dE = k dv / r2 = dE = k/r2 dv
Electric Field due to Continuous Charge Distribution
The charge dispersion is continuous rather than discrete. It divides the charges into small pieces and work on each piece like a point charge but due to the quantization of charge there is no such thing are as 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 a
Importance of Continuous Charge Distribution
For charging the devices, appliances require continuous charge distribution so that the battery is charged uniformly.
For the proper working of home appliances, continuous charge density plays important role. When the charge is non uniform then the appliance are not working properly.
Continuous charge distribution helps to store more energy.
Comparison Between Type of Charge Distribution
| Type of charge distribution | Line Charge | Surface Charge | Volume Charge |
|---|---|---|---|
| Denoted by | λ | σ | ρ |
| Value | ΔQ/ΔL | ΔQ/ΔS | ΔQ/ΔV |
| Unit | c/m | c/m2 | c/m3 |
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