Magnetic Field Strength (H)

Magnetic Field Strength, denoted by H, is a vector quantity that describes the intensity of a magnetic field produced by electric currents or magnetic sources. It is measured in amperes per meter (A/m) and represents the magnetizing force that induces magnetic flux in a material, independent of the material’s response.

Magnetic Field Strength vs. Magnetic Flux Density

Magnetic Field Strength (H) and Magnetic Flux Density (B) are related but distinct physical quantities:

B = μH, with μ = μ₀ × μᵣ

where:

• B: Magnetic flux density (T)

• H: Magnetic field strength (A/m)

• μ: Magnetic permeability of the medium

• μ₀: Permeability of free space (4π × 10⁻⁷ H/m)

• μᵣ: Relative permeability of the material

In magnetic materials, the relationship extends to:

B = μ₀(H + M)

where M is the magnetization vector representing the material’s internal magnetic response.

The unit of μ₀ (henrys per meter) ensures dimensional consistency:

B = μH → T = (H/m) × (A/m)

Formulas for Magnetic Field Strength

Straight Conductor

H = I / (2πr)

• I: Current (A)

• r: Radial distance from the conductor (m)
  Valid for infinitely long, straight conductors.

Solenoid

H = nI

• n: Number of turns per meter

• I: Current through the coil (A)
  Valid for long solenoids with air or nonmagnetic cores. H remains unchanged for magnetic cores.

Example Calculations

Air-core Solenoid

A solenoid with n = 200 turns/m and I = 3 A:

H = 200 × 3 = 600 A/m

In air (μᵣ ≈ 1):

B = μ₀H ≈ 4π × 10⁻⁷ × 600 ≈ 0.75 mT

Solenoid with Iron Core

If the same solenoid uses a ferromagnetic core with μᵣ = 5000:

B = μ₀μᵣH = 4π × 10⁻⁷ × 5000 × 600 ≈ 3.77 T

This illustrates how high-permeability materials amplify B without affecting H.

Applications

• Electrical engineering: Magnetic field design in transformers, motors, inductors

• Medical imaging: MRI systems generate static magnetic fields up to 1.5–3 T using high H from superconducting coils

• Materials science: Characterization of magnetic materials via hysteresis loops

• EMC compliance: Evaluation of field emissions and magnetic immunity in electronic systems