Question

Explain Coulomb's Inverse Square Law regarding the force between two magnetic poles.

Hint:

Coulomb’s law for magnetism is mathematically similar to electrostatic force. Replace electric charge with magnetic pole strength and permittivity with permeability.

Answer 1

Concept: Coulomb’s Inverse Square Law for magnetism describes the interaction between two magnetic poles (similar to electrostatic force between charges). It applies to ideal magnetic poles and helps quantify magnetic force. The law states that:
Like poles repel and unlike poles attract.
The magnitude of force depends on pole strength and distance between poles.
Statement of Coulomb’s Law (Magnetism): The force between two magnetic poles is:
Directly proportional to the product of their pole strengths.
Inversely proportional to the square of the distance between them.
Acts along the line joining the two poles.
Mathematical Expression: Let,
\( m_1, m_2 \) = pole strengths
\( r \) = distance between poles
Then, \[ F \propto m_1 m_2 \] \[ F \propto \frac{1}{r^2} \] Combining both relations: \[ F \propto \frac{m_1 m_2}{r^2} \] Introducing proportionality constant: \[ F = \frac{\mu_0}{4\pi} \cdot \frac{m_1 m_2}{r^2} \] where,
\( \mu_0 \) = permeability of free space
Nature of Force:
Attractive for unlike poles
Repulsive for like poles
Acts along the straight line joining the poles