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Charge density is the measure of electric charge accumulated per unit volume or per area of a surface of a body or field. The charge density formula helps to calculate how much charge is stored in a given field. Charge density can be determined in terms of area, volume, or length. Charge density formula is of 3 types – linear, volume, and surface charge density.
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Key Terms: Charge density, Electric charge, Electric field, Linear charge density, Surface charge density, Volume charge density, Field
Charge Density Formula
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Some of the basic formulas related to charge density are:
Linear Charge Density
- Linear charge density (λ) is the amount of charge per unit length, measured in coulombs per meter (C.m-1), at any point on a line charge distribution.
- If q is the charge and l is the length over which it flows, the linear charge density formula is given as –
λ = q/l
Surface Charge Density
- The surface charge density(σ) is the amount of charge per unit area, measured in coulombs per square metre (C.m-2), at any location on a two-dimensional surface.
- If q is the charge and an is the area of the surface over which it flows, the formula for surface charge density is –
σ = q/A
Read More: Continuous Charge Distribution
Volume Charge Density
- Volume charge density(ρ) is the amount of charge per unit volume at any location in a three-dimensional body. The SI unit is coulombs per cubic metre (C.m-3).
- If q is the charge and V is the volume over which it flows, the volume charge density formula is –
ρ = q/V
The meanings of the common symbols used in charge density formula are –
| Symbols | Meaning |
|---|---|
| λ | Linear Charge Density |
| σ | Surface Charge Density |
| ρ | Volume Charge Density |
| q | Electric Charge |
| l | Length |
| A | Area |
| V | Volume |
Charge Density Formula – Solved ExampleExample: Find the charge density when an 10C charge is present in a 5 m3 cube. Solution: Given- Charge q = 10 C, Volume v = 5 m3 The charge density formula is given by ρ = q/v = 10/5 Charge density ρ = 2 C/m3 |
Read Also:
| Charge Density Formula – Related Topics | ||
|---|---|---|
| Electric Charges and Fields | Gauss's Law | Electrostatics |
| Dipole in a Uniform External Field | Electric Dipole | Gaussian Surface |
| Unit of Electric Flux | Charging by Induction | Unit of Electric Charge |
Charge Density
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Charge density is a measurement of how much charge is stored in a given field. The density of a charge can be measured in terms of volume, area, or length. The electric charge per unit of space is measured by charge density. The measuring space can be one, two, or three-dimensional. Charge density, like mass density, changes with position. As a result, it can be either positive or negative.
Also Check:- Electric Charges and Fields: Important Questions
Applications of Charge Density
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The following are some examples of charge density applications:
- It appears in Maxwell's equations as well as the continuity equation for electric current.
- When the charge distribution moves, this equates to a current density, according to the electromagnetic field's major source term.
- The chemical and separation aspects of any process are both affected by the charge density of molecules. It has an impact on both metal-metal and hydrogen-metal bonds.
- In procedures like nanofiltration, the charge density of ions affects their rejection by the membrane.
- In the theory of special relativity, charge density is combined with current density.
Read Also:
Things to Remember
- The charge density is a measurement of how much electric charge has accumulated in a specific field.
- 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 per unit surface area, where q is the charge and A is the surface area. Coulomb m-2 is the SI unit.
- Volume charge density, where q is the charge and V is the distribution volume. Coulomb m-3 is the SI unit.
- Charge density mostly appears in Continuity Equation, Maxwell’s Equation, Nanofiltration, Special Relativity and so on.
Previous Years Questions
- Two long current carrying thin wires, both with current II, are held by insulating threads of length L….[JEE Main 2015]
- Let a total charge 2Q be distributed in a sphere of radius RR, with the charge density given by….[JEE Main 2019]
- In finding the electric field using Gauss law the formula...[JEE main 2020]
- For a uniformly charged ring of radius RR, the electric field on its axis has… [JEE Main 2019]
- Charge is distributed within a sphere of radius RR with a volume charge density…. [JEE Main 2019]
- An electric dipole has a fixed dipole moment...[JEE Main 2017]
- A thin disc of radius b=2a has a concentric hole of radius 'a ' in it….. [JEE main 2015]
- A spherically symmetric charge distribution is characterised by a charge density having the...[JEE Main 2014]
- A particle of charge q and mass mm is subjected to an electric field...[JEE Main 20202]
- A long cylindrical shell carries positive surface charge σ in the upper half and negative surface charge…..[JEE Main 2015]
- The value of A such that the electric field in the region between the spheres will be constant, is….[JEE Main 2016]
- Consider a sphere of radius R which carries a uniform charge density ρ…. [JEE Main 2020]
- An electric dipole is formed by two equal and opposite charges qq with separation… [JEE Main 2019]
- Two charges, each equal to q , are kept at x=−a and x=a on the…. [JEE Main 2013]
- A glass rod rubbed with silk is used to change a gold leaf electroscope and the leaves are observed to….[JEE Advance 2011]
- In the given circuit, what will be the equivalent resistance between the points A and B ?…. [JIPMER 2006]
Sample Questions
Ques. Is charge density a scalar or a vector? (1 marks)
Ans. As current density is a product of charge density and velocity, where charge density is a scalar quantity and velocity is a vector quantity, the current density is a vector quantity as well.
Ques. What effect does charge density have? (1 marks)
Ans: Chemical and separation processes are influenced by the charge density of molecules. Charge density, for example, has an impact on metal-metal bonding and hydrogen bonding. The charge density of ions determines their rejection by the membrane in separation techniques such as nanofiltration.
Ques. A total charge of 5mC is uniformly spread throughout a 50cm long thin rod. What is the charge density of a line? (2 marks)
Ans: q = 5 mC = 5 × 10-3 C
l = 50 cm = 0.5 m
In order to find λ, we know λ = q / l
So, λ = 5 × 10-3 / 0.5 = 10-2 c⋅m−1
Ques. A sphere has a radius of 9 cm and a charge of 12 C. How can you figure out the linear charge density? (2 marks)
Ans: Given data-
Charge q = 12 C and Radius r = 9 cm.
The surface charge density formula is given by σ = q / A
As, A=4 π r2
So, A will be = 4 π (0.09)2 = 0.1017 m2
Surface charge density, σ = q / A
So, σ = 12 / 0.1017 = 117.994
Hence, σ will be = 117.994 cm−2
Ques. A charge of -260e is equally distributed across the volume of a sphere with a radius of 1.85 cm. What is the volume charge density of the sphere? (2 marks)
Ans: Given,
Charge Q=−260e and Radius r=1.85cm
The volume charge density is given by the equation: If Q is the total charge spread over a volume V, then the volume charge density is given by the equation:
ρ= Q/V
The volume of a sphere V= 4/3πr3
The volume charge density of the sphere will be ρ = Q / (4/3)πr3
=−260e×3 / 4π(1.85cm)3
=−9.8ecm−3
Ques. If a charge of 8 C is contained in a 4 m3 cube, calculate the charge density. (2 marks)
Ans: Given :
Charge q = 8 C
Volume v = 4 m3
The charge density formula is given by ρ = q / v = 8 / 4
Charge density ρ will be = 2 C/m3
Ques. Calculate the Charge Density of an Electric Field when a charge of 6 C/m flows through a 3 m3 Cube. (2 marks)
Ans: Given Electric Charge, q = 6 C / m
Volume of the cube, V = 3 m3
The volume charge density formula is:
ρ = q/V
ρ =6/3
Charge density for volume ρ = 2C per m3.
Ques. Find the Volume Charge Density if a 10 C charge is applied over a 2m3 area. (2 marks)
Ans: Given,
Charge q = 10 C
Volume v = 2 m3.
The volume charge density formula is,
ρ = q / v
ρ = 10C / 2m3
ρ = 5C/m3
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