Continuous Charge Distribution

If the continuous charge of distribution is not properly distributed over the length of the conductor then this is called linear charge density and is denoted by lambda.

The unit of a linear load of density is C/m. If we find a conductor with a length of L with a surface load density and take a small length dl on it then a small charge dq will be on it.

  dq= λ dl,

Where λ is the line charge density,

dl is the small length of the conductor, and

dq is the charge of small length dl of a conductor.

Surface Charge Density

If the continuous charge of distribution is uniformly distributed over the conductor that is a surface charge of distribution then  it is also called as surface charge density. It is 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. Hence, there will be a small charge on the driver

dQ= σ ds

Volume Charge Density

If the charge is distributed over to the object’s  volume, it is volume charge distribution. It is denoted by the (rho) 𝜌 symbol.

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

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

dq = 𝜌dv

 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 quantized, there is no such thing as truly continuous charge distribution.

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

Continuous Charge Distribution due to the Electrostatic Force

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 referred to 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

Electric field for the 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.

Conclusion

In the continuous charge distribution system, the charge is uniformly distributed over the conductor. There are three types of charge distribution that are linear charge surface charge and volume charge, linear charge density, surface charge density and volume charge density.

In the electric field, due to continuous charge distribution, the charge dispersion is continuous. Electric field for continuous charge distribution can be obtained by the superposition principle and Coulomb’s law.

• The formula of linear charge density is  λ= ql, 

• The surface charge density σ of a wire is given as σ = 𝛥q𝛥s
  where Δs represents the area element of a charged sheet and Δq represents the charge contained in that area element

• The volume charge density ρ is given as ρ  = 𝛥q𝛥v

          where Δv represents the volume element of a charged sphere and Δq represents charge contained in that volume element.