The movement of charge in an electric field is always crucial to determine. In addition, electric charges will accumulate in such fields. As a result, charge density computation is critical for a variety of purposes. The charge density of an electric object must also be determined using the surface area and volume of the object. The surface charge density formula is a topic that is both significant and fascinating. The topic will be better understood if you use examples that are related to it. Let’s take a look at the concept!
What is Surface Charge?
The surface charge density describes the total amount of charge q per unit area A and is only seen on conducting surfaces.
The charge density is a measurement of how much electric charge has accumulated in a specific field. It calculates the quantity of electric charge based on the dimensions provided. The length, area, or volume of the electric body are all possible dimensions.
As a result, charge density can be one of three sorts. Charge density is a measure of electric charge per unit volume of space in one, two, or three dimensions, according to electromagnetism. There are three types of these:
- Charge density per unit length, i.e. linear charge density, where q is the charge and is the distribution length. Coulomb m-1 will be the SI unit.
- Surface charge density is defined as the charge per unit surface area, where q is the charge and A is the surface area. Coulomb m-2 is the SI unit.
- The charge density per unit volume, or volume charge density, where q is the charge and V is the distribution volume. Coulomb m-3 is the SI unit.
The amount of electric charge per unit surface area, in particular, is critical. Surface charge refers to the difference in electric potential between the inner and exterior surfaces of an item in various states. Only conducting surfaces will have a surface charge density, which describes the total amount of charge per unit area.
Formula for Surface Charge Density
The formula for surface charge density is:
σ = q/A
where,
- σ = Surface charge densityc(Cm-2),
- q = Chargec(C),
- A = Surface areac(m2)
Applications of Surface Charge Density
- Surface charge density is a fundamental quantity that is used to describe a variety of measurement-related phenomena.
- It’s utilized a lot in DNA hybridizations.
- It’s also useful for surface contact.
- Surface charge density can be used to assess biomolecular interactions that remain on surfaces, as well as to determine their quantification.
- Potentiometric titration, reflection interference contrast microscope, or atomic force microscopy can all be used to measure it.
- Surface Plasmon Resonance (SPR) is the most precise way of assessing surface charge density, according to a recent study.
Sample Problems
Problem 1: A total charge of 5 mC is uniformly spread throughout a long thin rod circular with a length of 60 cm and a radius of 7 cm. Calculate the charge density on the surface.
Solution:
Given : q = 5 × 10-3, l = 60 cm, r = 7 cm
Find : σ
Solution :
Surface area of cylinder = 2πrh
∴ Surface area of cylinder = 2 × 3.14 × 7 × 60
∴ Surface area of cylinder = 2637.6 sq cm = 2.63 sq m
We have,
σ = q/A
∴ σ = 5 × 10-3 / 2.63
∴ σ = 1.9011 × 10-3
∴ σ = 0.190 × 10-2 C/m2
Problem 2: Calculate the surface charge density of a conductor in a 30 m2 region with a charge of 2 C.
Solution:
Given : q = 2 C, A = 30 m2
Find : σ
Solution :
We have,
σ = q/A
∴ σ = 2 / 30
∴ σ = 0.066 C/m2
Problem 3: Calculate the charge density on the surface of a sphere with a charge of 9 C and a radius of 4 cm.
Solution:
Given : q = 9 C, r = 4 cm
Find : σ
Solution :
Surface area of Sphere = 4πr2
∴ Surface area of Sphere = 4 × 3.14 × 4 × 4
∴ Surface area of Sphere = 200.96 m2
We have,
σ = q/A
∴ σ = 9 / 200.96
∴ σ = 0.0447 Cm-2
Problem 4: Assume the conductor’s surface charge density is 0.23 C/m2 and the region is 13 m2. Determine the conductor’s charge.
Solution:
Given : σ = 0.23 C/m2, A = 13 m2
Find : q
Solution :
We have,
σ = q/A
∴ σ × A = q
∴ q = 0.23 × 13
∴ q = 2.99 C