## What is Charge Density?

The measure of electric charge accumulated in a particular field is called charge density. We can determine it in terms of volume, area, or length. We can divide the charge density formula into three types depending on its nature: (i) Linear (ii) charge density ( λ ) (iii) Surface charge density ( σ ) (iv) Volume charge density ( ρ ). Volume charge density is the quantity of charge per unit volume. Charge density measures the electric charge per unit measurement of the space. The space of measurement may be one, two, or three dimensional. Like mass density, charge density also varies with position. Thus, it can be positive or negative.

### What is Linear Charge Density?

The quantity of charge per unit length, measured in coulombs per meter (cm−1), at any point on a line charge distribution, is called linear charge density (λ).

Suppose q is the charge and l is the length over which it flows, then the formula of linear charge density is λ= q/l, and the S.I. unit of linear charge density is coulombs per meter (cm−1).

Example:

Q. A 50cm long thin rod has a total charge of 5mC uniformly distributed over it. What is the linear charge density?

Solution: q = 5 mC

= 5 × 10-3 C

l = 50 cm = 0.5 m

We have to find λ.

We know,

λ = q / l

= 5 × 10-3 / 0.5

= 10-2 c⋅m−1

### What is Surface Charge Density?

The quantity of charge per unit area, measured in coulombs per square meter (Cm−2), at any point on a two-dimensional surface, is called the surface charge density(σ).

Suppose q is the charge and a is the area of the surface over which it flows, then the formula of surface charge density is σ = q/A, and the S.I. unit of surface charge density is coulombs per square meter (cm−2).

Example:

Q. A sphere has a charge of 12 C and radius 9 cm. Calculate the linear charge density?

Solution: Given,

Charge q = 12 C,

Radius r = 9 cm.

The surface charge density formula is given by,

σ = q / A

A=4 π r2

A = 4 π (0.09)2

A = 0.1017 m2

Surface charge density, σ = q / A

σ = 12 / 0.1017

= 117.994

Therefore, σ = 117.994 cm−2

### What is Volume Charge Density?

The quantity of charge per unit volume, at any point in a three-dimensional body, is called volume charge density(ρ).

Suppose q is the charge and V is the volume over which it flows, then the formula of volume charge density is ρ = q / V and the S.I. unit of volume charge density is coulombs per cubic meter (C⋅m−3)

Example

Q.A sphere of radius 1.85 cm has a charge of -260e spread through the volume uniformly. The sphere has a volume charge density of?

Solution: We are given,

The charge in the sphere, Q=−260e

The radius of the sphere, r=1.85cm

If Q is the total charge distributed 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 is:

ρ = Q / (4/3)πr3

=−260e×3 / 4π(1.85cm)3

=−9.8ecm−3

### Solved Examples

1: Calculate the Charge Density of an Electric Field When a Charge of 6 C / m is Flowing through a Cube of Volume 3 m3.

Solution: Given the parameters are as follows,

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.

2: Find the Volume Charge Density if the Charge of 10 C is Applied Across the Area of 2m3.

Solution: Given,

Charge q = 10 C

Volume v = 2 m3.

The volume charge density formula is,

ρ = q / v

ρ = 10C / 2m3

ρ = 5C/m3

## FAQs on Charge Density Formula

- What are the Applications of Charge Density?

The various kinds of applications of charge density are given as follows:

- It appears in the continuity equation for electric current and also appears in Maxwell’s equations.
- According to the electromagnetic field’s principal source term, when the charge distribution moves, this corresponds to a current density.
- The charge density of molecules affects both the chemical and separation parts of any process. It influences both metal-metal bonding and hydrogen bonding.
- The charge density of ions influences their rejection by the membrane in processes such as nanofiltration.
- Charge density, along with current density, is used in the concept of special relativity.

- What is the Formula of Charge Density?

Charge density can be measured in terms of length, area, or volume depending on the body’s dimension. It is of three types, as follows:

- The quantity of charge per unit length, measured in coulombs per meter (Cm⁻¹), at any point on a line charge distribution, is called linear charge density ( λ ).

The formula of linear charge density is λ=q/l, such that q is the charge and l is the length of the body over which the charge is distributed.

- The quantity of charge per unit area, measured in coulombs per square meter (Cm⁻²), at any point on a two-dimensional surface is called the surface charge density(σ).

The formula of surface charge density is σ=q/A, such that q is the charge and A is the area of the surface over which it flows.

- The quantity of charge per unit volume, at any point in a three-dimensional body is called volume charge density ( ρ ).

The formula of volume charge density is ρ=q/v, such that q is the charge and v is the volume of the body over which it flows.

## Introduction

The flow of charge is very important for determining the electric field. They have a collection of electric charges. and thus charge density is very important to calculate for many purposes. The charge density is calculated based on the surface area and the volume of the electric object. The charge density formula is a very interesting and important topic.

The charge density is the measure of the accumulation of electric charge in a given particular field. The following are some of the dimensions in which the charge density is measured:

Charge density is based on the distribution of electric charge and it can be either positive or negative. The measure of electric charge per unit area of a surface is called the charge density.

### Example Problems

1. A long thin rod of length 50 cm has a total charge of 5 mC uniformly distributed over it. Find the linear charge density.

Solution:

q = 5 mC = 5 × 10^{–3} C, l= 50 cm = 0.5 m. λ= ?

2. A cuboidal box penetrates a huge plane sheet of charge with uniform surface charge density 2.5× 10^{–2} Cm^{–2} such that its smallest surfaces are parallel to the sheet of charge. If the dimensions of the box are 10 cm × 5 cm × 3 cm, then find the charge enclosed by the box.

Solution:

Charge enclosed by the box = charge on the portion of the sheet enclosed by the box.

The area of the sheet enclosed; A = area of the smallest surface of the box

## Charge Density Formula

For the electric field flow of charge is very important to determine. Also, such fields have an accumulation of electric charges. Thus charge density is very important to calculate for many purposed. Such charge density has to be calculated based on the surface area as well as the volume of the electric object. This topic of charge density formula is very important as well as interesting. Relevant examples will help to grasp the concept. Let us learn the concept!

The SI unit of Charge density is Coulomb per unit measurement under consideration.

The SI unit of Charge density is Coulomb per unit measurement under consideration.

**Solved Examples**

Q.1: Determine the charge density of an electric field, if a charge of 6 C per meter is

Q.2: A long thin rod of length 50 cm has a total charge of 5 mC, which is uniformly distributed over it. Find the linear charge density.

Solution:

Given parameters are:

### Volume Charge Density Solved Problems

**Question 1:** Find the volume charge density if the charge of 10 C is applied across the area of

**Sample Problems**

**Problem 1: Calculate the linear charge density of a surface if the charge is 2 C and length is 4 m. **

**Solution:**

We have,

q = 2

l = 4

Using the formula we have,

λ = q/l

= 2/4

=

0.5 Cm^{-1}

**Problem 2: Calculate the linear charge density of a surface if the charge is 5 C and the length is 3 m.**

**Solution:**

We have,

q = 5

l = 3

Using the formula we have,

λ = q/l

= 5/3

=

1.67 Cm^{-1}

**Problem 3: Calculate the charge if the linear charge density of a surface is 3 Cm ^{-1} and the length is 5 m.**

**Solution:**

We have,

λ = 3

l = 5

Using the formula we have,

λ = q/l

=> q = λl

= 3 (5)

=

15 C

**Problem 4: Calculate the surface charge density of a surface if the charge is 20 C and the area is 10 m ^{2}.**

**Solution:**

We have,

q = 20

A = 10

Using the formula we have,

σ = q/A

= 20/10

=

2 Cm^{-2}

**Problem 5: Calculate the charge if surface charge density of a surface is 5 Cm ^{-2} and the area is 20 m^{2}.**

**Solution:**

We have,

σ = 5

A = 20

Using the formula we have,

σ = q/A

=> q = σA

= 5 (20)

=

100 C

**Problem 6: Calculate the volume charge density of a surface if charge is 50 C and the volume is 80 m ^{3}.**

**Solution:**

We have,

q = 50

V = 80

Using the formula we have,

ρ = q/V

= 50/80

=

0.625 Cm^{-3}

**Problem 7: Calculate the charge if the volume charge density of a surface is 1 Cm ^{-3} and volume is 25 m^{3}.**

**Solution:**

We have,

ρ = 1

V = 25

Using the formula we have,

ρ = q/V

=> q = ρV

= 1 (25)

=

25 C

**Formula**

**Linear charge density is computed as:**

λ= q/l

**Surface charge density is computed as:**

σ= q/A

**Volume charge density is computed as:**

ρ= q/V

Where,

λ- Linear Charge Density

σ- Surface Charge Density

ρ- Volume Charge Density

A- Area

L- Length

V- Volume

**Solved Examples**

**Find the charge density if a charge of 8 C is present in a cube of 4**m3**.**

Given :

Charge q = 8 C

Volume v = 4 m3

The charge density formula is given by

ρ = q / v

= 8 / 4

Charge density ρ = 2 C/m3

**Determine the charge density of an electric field, if a charge of 6 C per metre is present in a cube of volume 3**m3**.**

Given parameters are as follows:

Electric Charge, q = 6 C per m

The volume of the cube, V = 3m3

The charge density formula computed for volume is given by:

ρ = q / v

ρ= 6/3

Charge Density Formula is ρ= 2C/m3.

### Charge Density Formula – Solved Example

**Example: **Find the charge density when an 10C charge is present in a 5 m^{3 }cube.

**Solution: **Given- Charge q = 10 C, Volume v = 5 m^{3}

The charge density formula is given by

ρ = q/v

= 10/5

Charge density ρ = 2 C/m^{3}

**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 r^{2}

So, A will be = 4 π (0.09)^{2} = 0.1017 m^{2}

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= 4/3πr^{3}

The volume charge density of the sphere will be ρ = Q / (4/3)πr^{3}

=−260e×3 / 4π(1.85cm)^{3}

=−9.8ecm^{−3}

**Ques. If a charge of 8 C is contained in a 4 m ^{3} cube, calculate the charge density. (2 marks)**

**Ans: **Given :

Charge q = 8 C

Volume v = 4 m^{3}

The charge density formula is given by ρ = q / v = 8 / 4

Charge density ρ will be = 2 C/m^{3}

**Ques. Calculate the Charge Density of an Electric Field when a charge of 6 C/m flows through a 3 m**^{3}** Cube. (2 marks)**

**Ans: **Given Electric Charge, q = 6 C / m

Volume of the cube, V = 3 m^{3}

The volume charge density formula is:

ρ = q/V

ρ =6/3

Charge density for volume ρ = 2C per m^{3}.

**Ques. Find the Volume Charge Density if a 10 C charge is applied over a 2m**^{3}** area. (2 marks)**

**Ans: **Given,

Charge q = 10 C

Volume v = 2 m^{3}.

The volume charge density formula is,

ρ = q / v

ρ = 10C / 2m^{3}

ρ = 5C/m^{3}

Mọi chi tiết liên hệ với chúng tôi :

**TRUNG TÂM GIA SƯ TÂM TÀI ĐỨC**

Số điện thoại tư vấn cho Phụ Huynh :

Điện Thoại : 091 62 65 673

Các số điện thoại tư vấn cho Gia sư :

Điện thoại : 0946433647 hoặc 0908 290 601

## Leave a Reply