Volume charge density represented using (ρ) is a measure of the amount of electric charge per unit volume in a given region of space. It is an important concept in electromagnetism and is used to describe how the charge is distributed within a three-dimensional object.

In this article, we have covered the charge density definition, volume charge density definition, formula and others in detail.

What is Charge Density?

Charge density is a measure of electric charge per unit length, surface area, or volume. It describes how charge is distributed in a given region of space and is crucial in understanding electrostatic fields and potentials

The charge density is categorized into three types:

• Linear Charge Density
• Surface Charge Density
• Volume Charge Density

Volume Charge Density

Volume Charge Density (ρ) is defined as the total charge Q divided by the volume V over which the charge is distributed. Volume Charge Density specifies how much amount of charge is present in the given volume. The electric charge can be represented by the Greek symbol pho (ρ).

Volume Charge Density Formula

Volume charge density tells us how much charge is present in a unit volume of a material. It is particularly useful in scenarios where the charge is not confined to a surface or a line but is spread throughout a volume, such as in solids, liquids, or gases. The formula to find the volume charge density is given by:

Volume Charge Density (ρ) = Charge (C)/Volume (V)

ρ = C/V

where,

• ρ is Charge Density
• C Represents Charge
• V is Volume in m³

Applications of Volume Charge Density

Various application of volume charge density includes:

In Electrostatics

• Volume charge density is used to calculate the electric field generated by a charge distribution using Gauss’s law.
• It helps in determining the potential and field inside and around charged objects.

In Capacitance

• In capacitors, understanding the volume charge density helps in analyzing the charge distribution between the plates.

In Plasma Physics

• Volume charge density is crucial in understanding the behavior of plasmas, which are ionized gases with free-moving charges.

In Material Science

• It helps in studying the electrical properties of materials, such as semiconductors and insulators.

Related Article:

• Current Density
• Continuous Charge Distribution
• Superposition Principle and Continuous Charge Distribution
• How to Calculate Current Density?

Examples on Volume Charge Density

Example 1: Find the volume charge density for the given charge and the volume is 8C and 12m³ respectively.

Solution:

Given,

• Charge (C) = 8
• Volume (V) = 12m³

Volume Charge Density (ρ) = C/V

= 8/12 = 0.66

Volume Charge Density for given data is 0.66 C/m³

Example 2: Find the volume charge density for the given charge and the volume is 18C and 9m³ respectively.

Solution:

Given,

• Charge (C) = 18
• Volume (V) = 9m³

Volume Charge Density (ρ) = C/V

= 18/9 = 2

Volume Charge Density for given data is 2 C/m³

Example 3: Find the charge for the given volume density charge and volume are 3 C/m³ and 6m³ respectively.

Solution:

Given,

• Volume charge density (ρ) = 3 C/m³
• Volume (V) = 6m³

Volume Charge Density (ρ) = C/V

Charge (C) = ρ×V

= 3×6 = 18

Charge for the given data is 18 C.

Example 4: Find the charge for the given volume density charge and volume are 2 C/m³ and 10m³ respectively.

Solution:

Given,

• Volume charge density (ρ) = 3 C/m³
• Volume (V) = 6m³

Volume Charge Density (ρ) = C/V

Charge (C) = ρ×V

= 2×10 = 20

Charge for the given data is 20 C.

Example 5: Find the Volume charge density for the given cube with side length 4m and the charge is 150C.

Solution:

Given

• Side length of cube = 4m

Volume of cube = side³

V = 4³ = 64

• Charge (C) = 150 C

Volume Charge Density (ρ) = C/V

= 150/64 = 2.34

Volume Charge Density for given data is 2.34 C/m³

Example 6: Find the Volume charge density for the given sphere with a radius of 2m and the charge is 50C.

Solution:

Given,

• Radius of sphere = 2m

Volume of sphere = (4/3)πr³

V = (4/3)π2³

= (4×22×8)/(7×3)

= 704/21 = 33.52

• Charge (C) = 50

Volume Charge Density (ρ) = C/V

= 50/33.52 = 1.49

Volume Charge Density for given data is 1.49 C/m³

FAQs on Volume Charge Density

What is Volume Charge Density in physics?

Volume charge density (ρ) is a measure of electric charge per unit volume. It quantifies how charge is distributed within a three-dimensional object. The formula is ρ = QV​, where Q is the total charge and V is the volume.

What are the Units of Volume Charge Density?

The units of volume charge density are coulombs per cubic meter (C/m³). This unit indicates how much charge is present in a unit volume of space.

How is Volume Charge Density Different From Surface and Linear Charge Densities?

Volume charge density (ρ) measures charge per unit volume (C/m³), surface charge density (σ) measures charge per unit area (C/m²), and linear charge density (λ) measures charge per unit length (C/m). They describe charge distribution in different dimensions.

Can Volume Charge Density be Negative?

Yes, volume charge density can be negative if the charge within the volume is negative. This indicates that the region has an excess of negative charge (electrons) compared to positive charge (protons).