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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!

Charge Density Formula

Source:en.wikipedia.org 

Charge Density Formula

What is charge density?

The charge density is the measure for the accumulation of electric charge in a given particular field.  It measures the amount of electric charge as per the following dimensions:

(i) Per unit length i.e. linear charge density, where q is the charge and is the length over which it is distributed. The SI unit will be Coulomb \(m ^ {-1}\).

(ii) Per unit surface area i.e. surface charge density, where, q is the charge and A is the area of the surface. The SI unit is Coulomb \(m ^ {-2}\).

(iii) Per unit volume i.e. volume charge density, where q is the charge and V is the volume of distribution. The SI unit is Coulomb \(m ^ {-3}\).

Charge density depends on the distribution of electric charge and it can be positive or negative. The charge density will be the measure of electric charge per unit area of a surface, or per unit volume of a body or field.

The charge density describes how much the electric charge is accumulated in a particular field. Mainly, it finds the charge density per unit volume, surface area, and length.

It measures the amount of electric charge per unit measurement of the space. This space may be one, two or three dimensional. Charge density will depend on the position, which can be negative.

Formula for Charge Density

(1)        Linear charge density is computed as:

\(\lambda = \frac {q} {l}\)

(2)        Surface charge density is computed as:

\(\sigma = \frac {q} {A}\)

(3)        Volume charge density is computed as:

\(\rho = \frac {q} {V}\)

Where

\(\lambda\) Linear charge density
\(\sigma\) Surface charge density
\(\rho\) Volume charge density
q Electric charge
A Area
L Length
V Volume

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 present in a cube of volume 3 \(m^3\).

Solution:

Given parameters are as follows:

Electric Charge, q = 6 C per m

Volume of the cube, V = 3 \(m^3\)

The charge density formula computed for volume is given by:

\(\rho = \frac {q} {V}\)

\(\rho = \frac {6} {3}\)

Charge density for volume \(\rho = 2 C per m^3\).

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:

q  = 5 mC = 5 \(\times 10 ^ {-3} \)

Length of the rod i.e. l = 50 cm = 0.5 m

The charge density formula computed for length is given by:

\(\lambda = \frac {q} {l} \)

= \(\frac {5 \times 10 ^ {-3}} {0.5} \)

= \(10^{-2} c; per; \)meter

Charge density for the length will be \(10^{-2} C; per; meter\).

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