Surface Charge Density Formula

According to electromagnetism, charge density is defined as a measure of electric charge per unit volume of the space in one, two, or three dimensions. To be specific, the linear surface or volume charge density is the amount of electric charge per surface area or volume, respectively.

Surface charge describes the electric potential difference between the inner and outer surface of different states like solid and liquid, liquid and gas, or gas and liquid. The surface charge density is present only in conducting surfaces and describes the whole amount of charge q per unit area A.

Formula of Surface Charge Density

The surface charge density formula is given by,

σ = q / A

Where,

• σ is surface charge density (C⋅m⁻²)
• q is charge {Coulomb(C)}
• A is surface area (m²)

Examples of Surface Charge Density

Example 1

Calculate the surface charge density of a conductor whose charge is 5 C in an area of 10 m²

Solution:

Given:

Charge q = 5 C,

Area A = 10 m²

Surface charge density formula is given by,

σ = q / A

= 5 / 10

Therefore, σ = 0.5 C/m²

Example 2

Calculate the surface charge density of the sphere whose charge is 12 C and radius is 9 cm.

Solution:

Given:

Charge q = 12 C,

Radius r = 9 cm.

The surface charge density formula is given by,

σ = q / A

For a sphere, area A = 4 π r²

A = 4 π (0.09)²

A = 0.1017 m²

Surface charge density, σ = q / A

σ = 12 / 0.1017

  = 117.994

Therefore, σ = 117.994 C⋅m⁻²