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Surface Charge Density Formula

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

Surface Charge Density Formula

What is surface charge density?

The charge density is the measurement for the accumulation of the electric charge in a given particular field.  It measures the amount of electric charge as per the given dimensions. Dimensions may be the length, area or volume of the electric body.

Thus charge density may b of three types. Therefore, according to electromagnetism, charge density is a measure of electric charge per unit volume of the space in one, two or three dimensions. Thus three kinds of these are:

(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 \(m ^ {-3}\)

Specifically, the amount of electric charge per unit surface area is much important.

Here, surface charge describes the electric potential difference between the inner and outer surface of different states of the object. The surface charge density will be there only in conducting surfaces and describes the whole amount of charge per unit amount of the area.

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.

The formula for Surface Charge Density:

Surface charge density is computed as:

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

Where,

\(\sigma\) Surface charge density
q Electric Charge
A Surface area

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

Solved Examples

Q.1: A long thin rod circular of length 50 cm and radius 7 sm has a total charge of 5 mC, which is uniformly distributed over it. Find the Surface 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

Radius of the rod = 7 cm

Thus the surface area of circulkar rod of cylinder shape, will be:

Surface Area of cylinder = \(2 \times \pi \times r \times h\)

= \(2 \times \frac{22}{7} \times 7 \times 50\)

= 2200 sq cm = 0.22 sq m

The charge density formula computed for length is given by:

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

= \(\frac {5 \times 10 ^ {-3} } { 0.22 }\)

= \(2.27 \times 10^{-2}\)

Surface charge density for the rod \(2.27 \times 10^{-2} C per m^{2}\)

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