Coulomb’s Law

Statement. The force between two point charges is directly proportional to the productg of the charges, and inversely proportional to the square of the distance between them.

The direction of the force will be along the line joining the two charges. The force is attractive if the two charges are of opposite nature and repulsive if the two charges are of the same type. The force depends on the nature of the medium in which the given two charges are situated.

Let q1 and q2 be two point charges situated at A and B separated by a distance r. r is the unit vector in the direction from A to B. Then the force (F12) exerted by charge q1 on charge q2 is

F₁₂ = C q1q1 r    ….. (1)
        ____r²  

where C is a constant. In SI units, C = 1/ (4П ε0)
when the charges are situated is vaccum. Here ε0 is called the permittivity of free space (i.e.,,vaccum).

The measured value of ε0 is
ε₀ = 8.85418x10^-12 C² N^-1 m-² (or Fm^-1).
This gives 1/ (4П ε₀) = 9 x 10⁹ Nm²C^-2.

When there is vacuum between the two charges, Coulomb’s law can be written as

F¹² =         1        q1 q2   r     …..(2)
           4П ε0           r²

Force exerted by q2 on q1 is equal and opposite to that exerted on q2 by q1 so that F12 = -F12.

If the charges are situated in a medium of permittivity ε, force between the charges is


F12 (m) =     1        q1 q2   r                       ..… (3)
           ___4П ε0           r2

Dividing eq. (2) by eq. (3), we get
  F12     = ε   = ε_r                                    ….. (4)
F12 (m) = ε₀
ε_r is called the relative permittivity of the medium, It is defined as the ratio of the permittivity of the medium to that of free space. εr is a dimensionless quantity. The value of εr for air is 1. To distinguish ε from εr we called the former the absolute permittivity of the material. The units of ε are Fm-1.s

In Eq. (2), if q1 = q2 = 1 and r = 1, we have
    F = (1/4П ε₀) q1 q2/ r² = (9 x 10⁹) 1X1/1² = 9 x 10⁹ N.

The SI unit of charge is the coulomb.
A coulomb is defined as the quantity of charge which, when placed at a distance of 1 meter in air or vacuum from an equal and similar charge, experiences a repulsive force of 9 x 10⁹ N.

A coulomb is also defined as the amount of charge that passes through any cross-section of a wire in 1 second if there is a current of 1 ampere in the wire.


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