Force between two magnetic poles
In 1785, Coulomb made use of his torsion balance and discovered the law governing the force between the two magnetic poles.
Coulomb?s inverse square law
Coulomb?s inverse square law states that the force of attraction or repulsion between the two magnetic poles is directly proportional to the product of their pole strengths and inversely proportional to the square of the distance between them.
If m1 and m2 are the pole strengths of two magnetic poles separated by a distance of d in a medium, then
F α m1m2 and F α 1/d2
F α m1m2/ d2
F = k m1m2/ d2
where k is the constant of proportionality and k = ?/ 4 π where ? is the permeability of the medium.
But ? = ?o ? ?r
?r = ? / ?0
where ?r - relative permeability of the medium
?o - permeability of free space or vacuum.
Let m1 = m2 = 1
and d = 1 m
k= ?0 / 4 π
In free space, ?o = 4π ? 10-7 H m-1
F = 10-7 ? m ? m /d2
F = 10-7 N
Therefore, unit pole is defined as that pole which when placed at a distance of 1 metre in free space or air from an equal and similar pole, repels it with a force of 10-7 N.