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 describes how much electric charge is accumulated in a particular field. Specifically, it finds the charge density per unit volume, surface area, and length. It measures the amount of electric charge per unit volume of space, in one, two or three dimensions. Charge density may depend on position, but it can be negative.

The SI unit of Charge density is C.

Charge density formula is given by,

σ = q / A

Where,

q = electric charge

A = area

Similarly, the volume charge density is given by,

ρv = q / v

Where,

q = electric charge

v = volume in m3

The charge density in terms of electric field is given by,

ρ = ϵo / E

Where

E = electric field

ϵo = permittivity

Example1

Determine the charge density of a field if the electric field of 100 N/C is applied across it.

Solution

Given parameter is,

Electric field E = 100 N/C

ϵo = 8.854 ×10−12 C/N

The Charge density, q is given by

q = ϵo E

= 8.854 × 10−12 × 100

= 1770.8 × 10-12C/m2

Example 2

Determine the charge density if a charge of 6 C/m is present in a cube of 3 m3.

Solution

Given parameters are

Charge q = 6 C/m

Volume v = 3 m3

The charge density formula is given by

ρv = q / v

= 6 / 3

Charge density = 2 C/m2