Electric charges and field Part - 3

Coulomb’s law:

According to Coulomb’s law the electrostatic force between two stationary point charges is directly proportional to the product of their magnitude and inversely proportional to the square of the distance between them. This force acts along the line joining the two charges which is repulsive if the charges have the same polarity and attractive if the charges have the opposite polarity.

If q₁ and q₂ are the two stationary point charges at rest and separated by a distance r, the magnitude of the force between them is F or, F = k.

In SI unit, in air or free space k = = 9 10⁹ Nm²C^-2 and is called permittivity of free space and it’s value is 8.854 10^-12 C²N^-1m^-2. So, F = .

In any other medium k = and is called permittivity of medium. So, F_m = .

In C.G.S. unit, in air or free space k = 1. So, F = ^.

In any other medium k = where K is called dielectric constant of the medium or relative permittivity. K = = . So, F_m = .

Vector form of Coulomb’s law:

Let q₁ and q₂ are the two stationary point charges are placed at point A and B where = and = , where O is the origin. and are the position vectors of A and B respectively.

The force acting on q₁ due to q₂ is = where r̂₁₂ is the unit displacement vector from q₂ to q₁. From OAB, + =

Or, + =

Or, _{= –} also = =

So, ₌ ———–(1)

Coulomb’s law follows Newton’s third law: [write the part Vector form of Coulomb’s law with diagram and continue this]

The force acting on q₂ due to q₁ is = where is the unit displacement vector from q₁ to q₂.

From OAB, + =

Or, + =

Or, _{= –} also = =

So, = = – ——-(using equation 1) So, Coulomb’s law follows Newton’s third law.

Principle of super position: Let us consider there is a system of point charges q₁, q₂, q₃ —— q_n having position vectors r₁, r₂, r₃ —— r_n respectively.The force acting on q₁ due to q₂ is F₁₂ =