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Coulomb’s Law- Definition, Explanation, Application, Scalar & Vector Form

If you rub amber with a cloth, the amber attracts the pieces of dry leaves. If you rub a glass rod with a silk cloth, the glass rod attracts the pieces of dry paper. If you rub a plastic rod with a woolen cloth, the plastic rod also attracts the pieces of dry paper. Although the different materials of the rod and the cloth are used, they show the same property. If you notice, you will find they attract each other more when they are brought closer. Do you know why ? Well, this is explained by Coulomb's law of attraction.

Table of contents: 

  • Coulomb’s Law in Scalar Form
  • Coulomb’s Law in Vector Form
  • Practice Problems
  • FAQs

Coulomb’s Law in Scalar Form:

Charles Augustine de Coulomb, a French engineer quantified the force between two point-charges in 1785. When the size of charged bodies are much smaller compared to the distance between them, they can be treated as point charges

The electrostatic force of interaction between two point-charges is directly proportional to the product of the magnitude of two charges and is inversely proportional to the square of the distance between the point-charges. The force acts along the line joining them.

If two point-charges of and are separated by , the force between them (in ) is given by, 

Coulomb used torsional balance for measuring the force. In the original experiments, it was established at a macroscopic scale but it has also been established at the range of subatomic level (). 

The choice of proportionality constant determines the size of the unit of charge. In SI unit the proportionality constant is about So two charged particles containing a magnitude of of charge each are separated by a distance of in vacuum attracts or repels each other with a force of . In practice we usually deal with smaller units of charges like or . The proportionality constant is expressed as where is the permittivity of free space 

So,

For media other than vacuum,

Where is known as the dielectric constant.

for vacuum, for air, for glass, for water, for conductor

Coulomb’s Law in Vector Form:

Let the position vectors of two point-charges be and .

(Electrostatic force on due to )

(Electrostatic force on due to )

directs towards from and directs towards from

if the sign of and are of same nature then the directions of and will be in the directions of and respectively i.e. they will be of repulsive nature. If the charges are of opposite nature, then the direction of and changes to and respectively i.e. attractive in nature. 

Here as []

Thus, Coulomb's law is in line with Newton's third law.

Practice Problems: 

Q. Three identical small balls (say A, B, C) made of conducting material are taken. A, B are charged and C is neutral. When A and B are placed 10 cm apart, they repel each other with force . Now C is touched with B and then A, C are placed 20 cm apart. The force between A, C will be . Find .

A. Let the charges in A, B be and respectively and  

Then  

Now C is touched with B and as a result they share the charge. As both of them are identical, they share the charge equally. 

So, the charge in C is

As stated,  

Q. Two point-charges are at a distance of . They are attracting each other with a force of . The charges in both of them are reduced to and of their original charges respectively. They are now brought nearer at a distance of . The electrostatic force now will be,

A. and

Q. A particle carrying charge revolves around another particle of charge . The radius of the circular path is . Show that the time period of revolution is proportional to .

A. Here the electrostatic attraction force is providing the centripetal force.

So,

i.e.

 

i.e.

Q. Two point-charges placed at small distance apart repel each other with in a vacuum. Now they are placed under water with dielectric constant . Everything remains the same. What will be the force now?

 A.

Now, in vacuum and in water 

So, (force in vacuum is )

FAQs:

Q. Which of them is correct?

a.

b.

c.

d. none of these

A.

Q. The electrostatic force between two point-charges at a distance is proportional to .

is equal to 

a. 1

b. 2

c. -1

d. -2

A.

Q. The electrostatic force between two point-charges increases to times when the charges are increased by and times.

a. times

b. times

c. times

d. times

A. times

is proportional to

Q. The electrostatic force between two point-charges increases to times when the separation between the charges is decreased to half.

a. times

b. times

c. times

d. times

A. times

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