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Surface Charge Density can be defined as the total amount of charge per unit area. It is essentially a measure of charge accumulation in a given electric field. It is denoted by σ. It is measured in coulombs per square metre (C/m2). It can be both positive and negative depending upon the charge taken into consideration.
Also Read: Gauss's Law
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Key Takeaways: Surface Charge, Charge, Electrons, Protons, Electric Field, Curvature, Magnetic field, Coulomb, Density, Electric Charge, Charge density
What is Electric Charge?
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Electric Charge is a property of a matter that specifies how its particles will behave in the influence of an electric or magnetic field. The SI unit of charge is Coulomb.
- If there exists a greater number of protons in a matter than the number of electrons, it is said to have a positive charge.
- If there exists a greater number of electrons in a matter than the number of protons, it is said to have a positive charge.
- If the number of protons and electrons are equal, the matter is said to have no charge (neutral).
- Electric Charge can either be positive or negative.
- It cannot be created or destroyed.
Electric Charges and their Nature
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What is Surface Charge?
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Surface Charge can be defined as a two-dimensional surface that possesses some charge in it. These charges are contained inside this surface. It basically signifies the difference in the electric potential that exists between the inner and outer surface of different matter, be it solid, liquid, or gas. This surface charge can only exist in the surface of matter that is conducting in nature.
Surface Charge
Also Read: Dipole in a Uniform External Field
Surface Charge Density
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Surface Charge Density is the surface charge (q) per unit area (A). This is a measure of how much charge is present in the unit area of the surface. It is denoted by a Greek Symbol called sigma (σ). It is dependent on the curvature of the conductor. More the curvature, the more the surface charge density. The SI unit of surface charge density is Coulomb per square metre.
Formula of Surface Charge Density
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σ = \(\frac{q}{A}\)
where,
σ = Surface Charge Density
q = Electrical Charge
A = Surface Area
Applications of Surface Charge Density
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Surface Charge Density has a range of applications. Some of it is listed down below:
- It is deployed in the calculation of field intensity at any given point in an electrostatic field.
- It plays a key role in the equilibrium distance between a charged particle and charged surface.
- It is a factor in the chemical and separation processes.
- It impacts bonding between metals and also the formation of hydrogen bonds.
Things to Remember
- The formula of surface charge density is σ = q / A.
- It can only exist over conductors of electricity.
- Electric Charges can be distributed along the length, surface or volume of the matter.
- It is not limited to one single conductor. Different conductors can have the same value of Surface Charge Density even if their charges are the same.
- This can happen when their surface areas are in proportion.
Also Read:
Sample Questions
Ques. What are the types of charge densities? (3 marks)
Ans. Charge density can be of 3 types. They are:
- Per unit length: This is called linear charge density.
In this case, q charge is distributed over length l.
Its SI unit is C/m
- Per unit surface area: This is called surface charge density.
In this case, q charge is distributed over surface area A.
Its SI unit is C/m2
- Per unit volume: This is called volume charge density.
In this case, q charge is distributed over volume V.
Its SI unit is C/m3
Ques. What will be the surface charge density of a sphere and a cylinder? (3 marks)
Ans.
- Sphere:
Charge = Q
Surface area of sphere = 4 π r2
σ = Q / 4 π r2
- Cylinder:
Charge = Q
Length = L
Surface area of each flat surface of sphere = π r2
σ (flat surface) = Q / 4 π r2
Surface area of curved surface = 2 π r L
σ (curved surface) = Q / 2π r L
Ques. What will be the surface charge density of an irregular shape? (3 marks)
Ans. In the case in which the surface area is different on each point of the surface of the conductor, the charge density will vary from point to point. Its value will be greater where the curvature is greater. This means that its value will be greater in the edges of the plane.
Hence, there is no fixed formula for calculating the value of surface charge density of a container of irregular shape.
Ques. In what way does the surface charge density vary in accordance to the curvature of the conductor? (3 marks)
Ans. Surface Charge Density varies according to the curvature of the conductor. It will be greater for greater values of curvature. This means that the edges of the conductor will possess greater surface charge density.
For example, consider a spherical conductor. The value of its surface charge density will be σ = Q / 4 π r2.
We know that when the curvature is higher, radius is lower.
In the above equation, the denominator will be smaller for a smaller radius.
This will result in a higher value of charge density.
Thus, it can be concluded that surface charge density increases with an increase in curvature.
Ques. What will be the surface charge density of a conductor if its charge is 10 Coulomb and its area is 20 m2. (3 marks)
Ans. Given,
Area = 20 m2
Charge = 10 C
Surface charge density can be calculated using the formula
σ = q / A
= 10 / 20
σ = 0.5 C/m2
Ques. Calculate the amount of charge on the surface of a spherical conductor if its radius is 10 cm and surface charge density is 0.7 C/m2. (3 marks)
Ans. Given,
surface charge density = 0.7 C/m2
Radius = 10 cm = 0.1 m
The area of the spherical conductor can be calculated with the formula
A = 4πr2 = { 4 × 3.14 × (0.1)2 }
A = 0.1256 m2
Thus, total charge on the conductor will be
Q = σ x A
= 0.7 x 0.1256
= 0.8792 Coulomb.
Ques. A thin circular rod has a total charge of 10mC which is uniformly distributed over it. If its radius is 5 cm and length is 50 cm, find its surface charge density. (4 marks)
Ans. Given,
Q = 10 mC = 10-2 C
Radius = 5 cm = 0.05 m
Length = 50 cm = 0.5 m
Surface area of cylinder = 2 × π × r × h
= 2 x 3.14 x 0.05 x 0.5
= 0.157 m2
Thus, the surface charge density will be
σ = q / A
= 10-2 / 0.157
= 6.37 x 10-2 C/m2
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