Charge Distribution

There are two types of charge distribution :

1. Discontinuous Charge Distribution,

2. Continuous Charge Distribution  

1. Discontinuous Charge Distribution : 

In this distribution the  charge is distributed randomly (non uniformaly) in a body at different places.

 2. Continuous Charge Distribution : 

In this distribution the  charge is equally distributed in a body at different places.

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

a) Linear Charge Distribution (λ) :

It is also known as linear charge density (λ), and it is defined as charge per unit length. 

λ=charge/length= ΔQ /Δl

It's unit is C/m.

Examples: charged straight wire, charged circular ring etc.

b) Surface  Charge Distribution (σ) :

It is also known as surface charge density (σ), and it is defined as charge per unit area. 

σ=charge/area= ΔQ /ΔS

It's unit is C/m^2.

Examples : charged plane sheet, charge conducting sphere etc.

c) Volume Charge Distribution (𝛿) :

It is also known as volume charge density (ρ), and it is defined as charge per unit volume. 

ρ=charge/volume= ΔQ/ΔV

It's unit is C/m^3

Examples : charged insulating sphere etc.

Area Vector :  By convection the area element vector ΔS at a point on a closed surface equals ΔS ˆn (n-cap) where ΔS is the magnitude of the area element and ˆn (n-cap) is a unit vector in the direction of outward normal at that point.

                                       

Fig. Convention for defining normal ˆn and ΔS.