Continuous Charge Distribution: Learn its Definition, & Types

Divya Kare | Updated: Sep 6, 2022 17:55 IST

Charge on surfaces is not always discreet. In real-world use, mostly the charge is spread over a surface. In such situations to calculate the phenomena due to such charge, the concept of charge density is taken into account. Charge density is actually the ratio between the total charge present on the surface and the area of the surface. Charge density is considered only in cases where a continuous charge is distributed over a length or surface of an object. The continuous charge distribution is of three types; Linear, Surface and Volume.

Read on to learn more about its concept and types.

Continuous Charge Distribution

Continuous charge distribution can be defined as the ratio between the charge present on the surface of any object and the surface over which the charge is spread.

In actuality, when charges are spread on any surface the number of electrons is so much that the quantum nature of electrons and the charge carried by each electron are not taken into account. The phenomenon of charge distribution comes into play in these situations. It is the amount of charge present on the surface.

Types

Continuous charge distribution can be categorized into different types based on the type of surface.

  • Linear Charge Distribution

When the charge is distributed on a linear object then the charge distribution is known as linear charge distribution. It can be mathematically stated as

\(\lambda = \frac{\Delta{Q}}{\Delta{l}}\)

Where,

\(\Delta Q \) = Charge present on the surface

\(\Delta l \)= length of the linear object

It is given in the units of charge per unit length which is \(cm^{-1}\).

  • Surface Charge Distribution

When the charge is distributed over a surface then the charge distribution is known as surface charge distribution. It can be mathematically stated as

\(\sigma = \frac{\Delta{Q}}{\Delta{s}}\)

Where,

\(\Delta Q \) = Charge present on the surface

\(\Delta s \)= surface area of the object

It is given in the units of charge per unit area which is \(cm^{-2}\).

  • Volume Charge Distribution

When the charge is distributed over a volume of any object then the charge distribution is known as volume charge distribution. It can be mathematically stated as

\(\rho = \frac{\Delta{Q}}{\Delta{v}}\)

Where,

\(\Delta Q \) = Charge present on the surface

\(\Delta v \) = volume of the object

It is given in the units of charge per unit volume which is \(cm^{-3}\).

Electric Field due to Continuous Charge Distribution

The electric charge due to a continuous charge distribution at a point P which is at a distance 'r' can be calculated in the following way. The instantaneous charge density at different points may be different. For that reason, the entire charge distribution is broken down into smaller elements. Let one such small volume element be \(\Delta v \) which has a charge distribution given by \(\rho\). The total charge in the specific volume element would then be equal to \( \rho \Delta v \). Then according to the Coulomb's Law, the electric field due to this charge element would be equal to

\(E = \frac{1}{4\pi\epsilon_{0}}\frac{\rho\Delta{v}}{r^{2}}\vec{r}\)

The total electric field due to the entire charge distribution would be the summation of all the charge elements :

\( E = \frac{1}{4\pi\epsilon_{0}}\displaystyle\sum_{all\Delta{v}}\frac{\rho\Delta{v}}{r^{2}}\vec{r}\)

Hope this article about Continuous Charge Distribution was able to convey to you the concept regarding this topic. There are many such interesting Physics topics and their real-life applications to learn about, just download the Testbook app and start browsing to get insights on them which can clear all your concepts regarding them.

FAQs

Q.1 What is the continuous charge distribution formula?

Ans.1 The continuous charge distribution formula is \(\sigma = \frac{\Delta{Q}}{\Delta{s}}\) for surface charge distribution.

Q.2 What are the different types of charge distributions?

Ans.2 The different types of charge distribution are Linear charge distribution, surface charge distribution and volume charge distribution.

Q.3 Why do we need continuous charge distribution?

Ans.3 Charge distributions are needed because when charges are spread on any surface the number of electrons is so much that the quantum nature of electrons and the charge carried by each electron is not taken into account. The phenomenon of charge distribution comes into play in these situations.

Q.4 What is the difference between a discrete and continuous charge distribution?

Ans.4 In discrete charge distribution the individual charge on the electrons is taken into account whereas in continuous charge distribution a large number of electrons are spread out on a particular surface.

Q.5 What is the importance of continuous charge distribution?

Ans.5 In real-life applications, it is required in appliances such as chargers because the battery needs to be charged uniformly.

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