The Two Laws of Magnetism

1. Definition

The Two Laws of Magnetism describe how magnetic poles interact and how magnetic force depends on distance and pole strength:

  • First Law Like poles repel; unlike poles attract.

North ↔ North → Repel South ↔ South → Repel North ↔ South → Attract

First Law of Magnetism Diagram

  • Second Law The force between two magnetic poles is directly proportional to the product of their pole strengths and inversely proportional to the square of the distance between them.

1.1. Second Law In Formula Form

Coulomb’s Law of Magnetism: F = (μ / 4π) × (m₁ · m₂) / r²

Where:

  • F : Magnetic force between poles
  • μ : Permeability of the medium (μ₀ in vacuum ≈ 4π × 10⁻⁷ H/m)
  • m₁, m₂ : Magnetic pole strengths (in Ampere-meter, A·m)
  • r : Distance between poles (in meters) Note : μ₀ / 4π : is the magnetostatic Constent, where μ₀ is the permeabilioty of free space (vacuum), use μ₀ when the magnetic interaction is happening in free space, wile μ is used when the medium is not air, like inside iron or another magnetic material!

1.2. Other Variations

  • Same pole types → Repulsion
  • Opposite pole types → Attraction
  • Force magnitude changes with medium (air, iron, etc.)
  • The law is similar in form to Coulomb’s Law but for magnetic poles

Two Laws of Magnetism Diagram

1.3. Unit of Measurements

  • Force (F): Newton (N)
  • Magnetic pole strength (m): Ampere-meter (A·m)
  • Distance (r): meter (m)
  • Permeability (μ): Henry per meter (H/m)

1.4. Example

If m₁ = 4 A·m, m₂ = 6 A·m, r = 0.2 m, and μ₀ = 4π × 10⁻⁷ H/m:

F = (4π × 10⁻⁷ / 4π) × (4 × 6) / (0.2²) F = (10⁻⁷) × (24) / 0.04 F = (2.4 × 10⁻⁶) / 0.04 F = 6 × 10⁻⁵ N

2. Usage

2.1. Calculations

The Two Laws of Magnetism help you:

  • Predict whether two magnetic poles will attract or repel
  • Calculate the magnitude of the force between poles
  • Determine the effect of distance and medium on force

2.2. Applications

They are used in:

  • Designing electromagnets and permanent magnets
  • Understanding compass operation and Earth’s magnetic field
  • Magnetic levitation systems
  • Magnetic separation in industries

3. Limitations

It is important to note that the Two Laws of Magnetism have the following limitations:

  • They apply to ideal magnetic poles, which don’t exist in isolation (magnetic monopoles have not been observed)
  • They are valid for short distances compared to the magnet size
  • They do not explain the origin of magnetism (which requires atomic-level theory)

4. Video Explanation

video coming soon