1) Coulomb's law describes the force between two point charges and states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. 2) Charles Coulomb experimentally deduced this law in 1784 to quantify the electric force. 3) The force between charges can be reduced by placing an insulating dielectric medium between them, with the reduction factor being the relative permittivity of the material.

1. CHP#12
ELECTROSTATICS
12.1 Coulombs Law

2. Electrostatics:
 “The study of electric charges at rest under the action of electric forces is known
as electrostatics.”
Electric Charge:
 Charge is the intrinsic property of fundamental particles.
 The property of certain particles either they attract or repel each other is termed
as charge.
 Charges are of two kinds: positive charges and negative charges.
 It has been experimentally found that like
charges repel each other and unlike charges
attract each other.

3.  Charge is quantized Q=ne
 The SI unit of electric charge is “coulomb”.
Electric force:
 The attraction or repulsion is due to electric force.
 The force which holds the positive and negative charges to make up atoms and
molecules is called an electric force.
 Our body is composed of atoms and molecules and our existence is result of electric
force.

4. Coulomb’s law
 “The force of (attraction or repulsion) between two point charges is directly proportional
to the product of the magnitude of charges and inversely proportional to the square of
the distance between them.”
 The first attempt to measure the force between
electric charges was made by a French
military engineer Charles Coulomb in 1784.
He deduced a law known as Coulomb’s law.
Explanation:
 Consider two point charges “q1” and “q2” placed at a distance “r” from each other. Then
magnitude of mutual force according to coulomb’s law is given by:

5. 𝑭 ∝ 𝒒𝟏𝒒𝟐
𝑭 ∝
𝟏
𝒓𝟐
𝑭 ∝
𝒒𝟏𝒒𝟐
𝒓𝟐
𝑭 = 𝒌
𝒒𝟏𝒒𝟐
𝒓𝟐
 Where k is constant of proportionality called electrostatic constant
Dependence of K
Its value depends upon
 The system of units
 Nature of medium the

6. For free space
 If the medium between two points charges is free space, then
𝐤 =
𝟏
𝟒𝛑𝛆𝐨
= 𝟗 × 𝟏𝟎𝟗𝐍𝐦𝟐𝐂−𝟐
 Where 𝜺∘ is an electrical constant, known as permittivity of free space
 In S.I units its value is 8.85 x 10-12 C2N-1m-2.
 Thus Coulomb’s force for free space is:
𝑭 =
𝟏
𝟒𝝅𝜺𝒐
𝒒𝟏𝒒𝟐
𝒓𝟐

7. Mutual force:
 F is the magnitude of mutual force that act on each of two point charges
 The force F always acts along the line joining the two point charges.
 As coulomb is mutual force thus charges q1 and q2 exerts equal and opposite forces on
each other.
Vector form:
 If the force exerted on q2 by q1 is denoted by 𝐹21 and that on charge q1 due to q2 as 𝐹12
then,
𝑭𝟏𝟐 = −𝑭𝟐𝟏

8.  The magnitude of these two forces is same but negative
sign show that they point in opposite direction.
 If 𝑟21is the unit vector directed from q1 to q2 and 𝑟12 is the unit
vector directed from q2 to q1, then forces are given as,
𝑭𝟐𝟏 =
𝟏
𝟒𝝅𝜺𝒐
𝒒𝟏𝒒𝟐
𝒓𝟐 𝒓𝟐𝟏
𝑭𝟏𝟐 =
𝟏
𝟒𝝅𝜺𝒐
𝒒𝟏𝒒𝟐
𝒓𝟐 𝒓𝟏𝟐
as 𝒓𝟐𝟏 = −𝒓𝟏𝟐
then
𝑭𝟐𝟏 =
𝟏
𝟒𝝅𝜺𝒐
𝒒𝟏𝒒𝟐
𝒓𝟐 −𝒓𝟏𝟐 = −
𝟏
𝟒𝝅𝜺𝒐
𝒒𝟏𝒒𝟐
𝒓𝟐 𝒓𝟏𝟐 = −𝑭𝟐𝟏
 The sign of charges represents either the forces are attractive or repulsive.
 This also implies that coulomb law is in accordance of Newton third law.

9. Effect of medium on Coulomb force:
 If an insulating medium called as dielectric is placed between the two charges, then it is
experimentally observed that the force is reduced as compared to free space.
 The factor by which the force is reduced is called relative permittivity and is denoted by
 Thus the force between charges in the presence of dielectric is given by:
Hence 𝐅𝐦𝐞𝐝 =
𝐅𝐚𝐢𝐫
𝛆𝐫

10.  The value of relative permittivity is different for different dielectrics.
 The value of 𝜀𝑟 is always greater than one.
 For air 𝜀𝑟 is 1.0006.
 It has no unit and hence it is a dimensionless quantity.
Permittivity:
 “The ability of a medium to allow the electric force to pass through it is determined by a
factor known as permittivity.
Relative permittivity:
 It is ratio between permittivity of medium to the permittivity of free space
Point charge:
 A charge is said to be a point charge if its size is very small as compared to the distance
from any other charge.