Coulomb’s Inverse Square Law (for Magnetic Poles):
Coulomb’s inverse square law states that the force of attraction or repulsion between two isolated magnetic poles is directly proportional to the product of their pole strengths and inversely proportional to the square of the distance between them.
Statement of the Law:
If two magnetic poles of strengths m₁ and m₂ are separated by a distance r in air (or vacuum), then the force F between them is given by:
F ∝ m₁m₂
F ∝ 1/r²
Combining both proportionalities,
F ∝ (m₁m₂)/r²
Introducing a constant of proportionality,
F = (μ₀/4π) × (m₁m₂ / r²)
Where μ₀ is the permeability of free space.
Nature of the Force:
• The force is attractive if the poles are unlike (north and south).
• The force is repulsive if the poles are like (north–north or south–south).
Important Features:
1. The force decreases rapidly as the distance increases, since it depends on 1/r².
2. The force acts along the straight line joining the two magnetic poles.
3. The law is similar in form to Coulomb’s law of electrostatics.
Conclusion:
Thus, according to Coulomb’s inverse square law, the force between two magnetic poles depends on the magnitude of their pole strengths and decreases inversely with the square of the distance between them.