Superposition Principle and Continuous Charge Distribution

Superposition Principle and Continuous Charge Distribution - Detailed Guide

Edited By Team Careers360 | Updated on Nov 12, 2024 11:18 PM IST

In this article, we will learn about the law of superposition which is also known as the principle of superposition.
Note: Superposition theorem in hindi is अध्यारोपण प्रमेय

What is superposition?/superposition meaning:

Overlapping one thing over the other is called the superposition.

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Superposition Principle and Continuous Charge Distribution - Detailed Guide

What is principle of superposition?/superposition principle in electrostatics/define principle of superposition

The principle of superposition states that the total force on a charge due to a number of other charges is given by the vector sum of the Coulomb forces exerted on the charge due to each of the other charges acting separately. This law is also known as the principle of superposition of forces.

Let us consider , there are N no of point charges like q1,q2,q3,q4,…….,qN.The total force acting on charge q for N no of charges is the sum of the individual forces F1,F2,F3,F4…..FN .So, the total force on the charge q is

F=F1+F2+F3+F4+…+FN=i=1NFi

The superposition principle is used in the calculation field, flux, potential energy of an electrostatic system.

Let us consider an example,

According to Coulomb’s law, the force between two charges be,

According to Coulomb’s law, the force between two charges

F=14π0.Q.qr2.r

Here,

F = total force

Q = test charge

q = point charge

r = distance between two charges

The principle of superposition can be shown with a minimum of three charges, but this principle is used for a large number of charges or N number of charges. In the below example, we will discuss the superposition principle

superposition principle

According to the diagram,

F1=14π0Q.q1r12r1

F2=14π0Q.q2r22r2

According to the principle of superposition

FQ=14π0[Q.q1r12+Q.q2r22]r

Here , Q = test charge ; q1=q2= point charge; r1= distance between the test charge and q1 charge ; r2= distance between the test charge and q2 charge ;r = the direction of the resultant force ; FQ= resultant force .

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Continuous charge distribution:

As we know, charge carried by a body is always an integral multiple of the smallest unit of charge which is a charge of an electron. According to this theory of quantisation of charge, it can be said that an electron has the smallest charge.

When the charges are very closely bound to each other then that type of charge distribution is known as continuous charge distribution.

According to the principle of superposition of charges, here are three types of continuous charge

linear charge distribution
Surface charge distribution
Volume charge distribution

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1. Linear charge distribution:

When the charges are distributed uniformly in one dimension or along length then this type of charge distribution is known as linear charge distribution.

2. Surface charge distribution :

When the charges are distributed uniformly in two dimensions or along a surface then this type of charge distribution is known as surface charge distribution.

3. Volume charge distribution :

When the charges are distributed uniformly in three dimensions or along a volume then this type of distribution is known as volume charge distribution.

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NCERT Physics Notes: