What is Surface Charge Density?

Surface Charge Density (σ) gives a measure of how the electric charge is distributed over an area. It is very useful in the analysis of conductors and insulators where charges are not all spread uniformly. If an electric charge has been carried on the surface, then it has a significant effect on the way in which the electric fields behave around it.

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

Formula

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)

Solved Problems 

Problems 1:Compute 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

So, σ = 0.5 C/m2

Problem 2: Find 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 formula of surface charge density is,

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

Thus, σ = 117.994 C⋅m−2

 

Other Related Sections

NCERT Solutions | Sample Papers | CBSE SYLLABUS| Calculators | Converters | Stories For Kids | Poems for kids| Learning Concepts I Practice Worksheets I Formulas | Blogs | Parent Resource