Surface Charge Density Formula

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What is Surface Charge Density

According to electromagnetism, surface charge density is known as the amount of electric charge in per unit length, volume or surface area. Volume charge density is known as the charge per unit of the quantity that is measured in the SI system as coulombs per cubic meter at any given volume. It is the charge per unit of the area on a two-dimensional surface.  Linear charge density is referred to the quantity of the charge per unit length and it is measured in coulombs per meter in a line distribution. 

Define Surface Charge Density 

The measurement for the accumulation of electric charge in a respective field is known as surface charge density. It helps in measuring the total quantity of electric charge as per the given dimension although dimension can be the area, length or volume of the electrical body. Surface charge density can be of three types. For understanding how to find surface charge density,  you must know that it is the measurement of the electrical charge in per unit of the space in one, two as well as three dimensions. These three kinds can be the following:

1. Per unit length area, for example, the linear charge density, in which q is known to be the charge and also the length on which it is dispersed. The SI unit is supposed to be m-1.

2. Per unit surface area, for example, the surface charge density in which q is referred to charge and A is known as the area of the respective surface. The SI unit here is Coulomb m-2.

3. Per unit volume, for example, volume charge density where V is the volume of the given surface and q is the charge. The SI unit of the Coulomb is m-3.

The most important objective to find the surface charge density is the amount of electric charge per unit of the surface area. 

Surface Density Formula

Surface charge density is:

σ= qAσ = qA


σ = surface charge density

q = electric charge

A = surface area

Surface Charge Density Equation 

The formula of surface charge density involves measurement from the total amount of electric charge accumulated over a surface area of a given object. It can be calculated by the charge per unit of the surface area. 

In the surface density of charge formula, “q” is known as the charge of the object and A is the total area of the surface. And then the surface area of the charge density is given by: 

σ= qAσ = qA

And the SI unit of the surface charge density is Cm-2.

The Formula of Surface Density: A Brief Explanation

According to the formula for surface charge density, charge density varies with the position just like mass density. As per the electromagnetic theory, the charge density functions as the continuous scalar function of position X as the fluid and p(x) are regarded as continuous charge distributions although all the real charge distributions are made up of discrete charged particles. All the charges are carried by subatomic particles.


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FAQ (Frequently Asked Questions)

1. Assume a Conducting Sphere of Radius 5 cm is Connected to 1000 V Power Supply. What is the Charge Density on the Surface of the Sphere C/m²C/m²?

Given data:

  • The radius of the sphere is: Rs=5cm=0.05m Rs=5cm=0.05m.

  • The voltage of the power supply is V=1000VV=1000V.

The expression to calculate the surface area of the sphere is given by,


Substitute all the values in the above expression.


The expression to calculate the charge on the sphere is given by,


Here, kk is coulomb's law constant whose value of 9×109N⋅m²/C9×109N⋅m²/C.

Substitute all the values in the above expression.


The expression to calculate the charge density on the surface of the sphere is given by,


Substitute :


Thus, the charge density on the surface of the sphere is 1.77×10−7C/m² 1.77×10−7C/m².

2. What are the Applications of Surface Charge Density?

Surface charge density is used as a basic quantity for various measurement-related phenomena. It is actively used in DNA hybridizations. It finds its use in surface interaction also. Biomolecular interactions that continue on surfaces can be measured with surface charge density and their quantification can also be calculated through it. It can be measured by potentiometric titration, reflection interference contrast microscope or atomic force microscopy. However, as per the latest research works, Surface Plasmon Resonance (SPR) method is the most accurate method of measuring surface charge density.