Charge Density Formula

The charge density is the measure of electric charge per unit area of a surface, or per unit volume of a body or field.

The charge density tells us how much charge is stored in a particular field. Charge density can be determined in terms of volume, area, or length.

Depending on the nature of the surface charge density is given as the following

Linear Charge Density

$\lambda =q/l$

where q is the charge and l is the length over which it is distributed

S.I unit of Linear charge density is coulomb/m

Surface Charge Density

σ = q / A

where q is the charge and A is the area over which it is distributed

S.I unit of Linear charge density is coulomb/$m^{2}$

Volume Charge Density

ρ = q / v

where q is the charge and V is the volume over which it is distributed

S.I unit of Linear charge density is coulomb/$m^{3}$

Solved Example

Find the charge density if a charge of 8 C is present in a cube of 4 m3

Solution

Given :

Charge q = 8 C

Volume v = 4 m3

The charge density formula is given by

ρ = q / v

= 8 / 4

Charge density ρ = 2 C/m3