Charge Density Formula For Volume, Surface & Linear With Solution

Charge Density Formula

For the electromagnetism, the charge density is defined as the total amount of charge carried for a particular length, area, or the volume. The symbol Pho (ρ) is used to denote the electric charge and subscript (v) is added to indicate the volume charge density.

Volume Charge Density Formula

Here, is given the volume charge density formula for your reference –

\[\ \huge q=int\, \rho\, dv\]

Where,ρ is charge density,dv is change in volume.The formula can also be written in a simple term as shown below.

\[\ \huge \rho =\frac{q}{v}\]


q is the charge,v is the total volume in m3.

Surface Charge Density Formula

Here, is given the surface charge density formula for your reference –

σ = q / A.


q = charge and

A = surface area.

Electric field regarding surface charge density formula is given by,

σ = -2 ϵ0 E.


ϵo = permittivity of free space,

E = electric field.

Linear Charge Density Formula

Here, is given the linear charge density formula for your reference –

\[\ \lambda {q} = \frac{dq}{dl} \]

λq = Linear charge density (C/m)
dq = derivative of the charge function (C)
dl = one dimension of the wire (the position along its length) (m)

Let us take the example of special relativity to understand the concept deeper. Here, the length of a wire generally depends on the velocity of observer because length is contracted and the charge density is directly related to the velocity. You must have heard of how magnetic field forces for a current-bearing wire increases when relative charge density increases. He used the pho diagram to explain the concept and how much charge density is carried by a moving frame.

Further, the concept of charge density is also applicable to maintain the continuity of the electric current and it can also be used for Maxwell equations too. It is generally defined as the source of electromagnetism field where the charge distribution is maintained evenly as per the current density level. Additionally, the charge density is also impacting the chemical or mechanical separation processes of molecules.

Take an example, where charge density directly influences the hydrogen bonding ormetal-metal bonding. For the separation processes like nanofiltration, the charge density of ions will influence the rejection by membrane as well.