Magnetic Permeability Calculator
Calculate magnetic permeability, relative permeability, and magnetic susceptibility relationships
Calculate Magnetic Properties
Absolute magnetic permeability of the material
Magnetic Properties Results
Absolute Permeability
μ: 0.000e+0 H/m
μ: 0.000e+0 μH/m
μ: 0.000e+0 nH/m
Relative Properties
μᵣ: 0.000000
χ: 0.000e+0
Type:
Relationships
μ = μᵣ × μ₀: 0.000e+0 = 0.000000 × 1.257e-6
χ = μᵣ - 1: 0.000e+0 = 0.000000 - 1
μ₀ (free space): 1.257e-6 H/m
Common Material Examples
Diamagnetic Materials
Water: μᵣ ≈ 0.999991
Copper: μᵣ ≈ 0.999994
Gold: μᵣ ≈ 0.999996
Bismuth: μᵣ ≈ 0.999834
χ < 0, weakly repelled
Paramagnetic Materials
Aluminum: μᵣ ≈ 1.000022
Magnesium: μᵣ ≈ 1.000012
Titanium: μᵣ ≈ 1.00018
Oxygen: μᵣ ≈ 1.000002
χ > 0 (small), weakly attracted
Ferromagnetic Materials
Iron: μᵣ ≈ 200-5000
Nickel: μᵣ ≈ 100-600
Cobalt: μᵣ ≈ 250
Mu-metal: μᵣ ≈ 80,000
χ ≫ 0, strongly attracted
Key Formulas
Permeability Relationship
μ = μᵣ × μ₀
Absolute = Relative × Free space
Susceptibility
χ = μᵣ - 1
Susceptibility from relative permeability
Magnetic Fields
B = μH
Magnetic flux density
Free Space Constant
μ₀ = 4π × 10⁻⁷ H/m
Permeability of vacuum
Unit Conversions
Understanding Magnetic Permeability
What is Magnetic Permeability?
Magnetic permeability (μ) is a measure of how easily a magnetic field can pass through a material. It describes the material's ability to support the formation of a magnetic field within itself. Materials with high permeability are easily magnetized and enhance magnetic fields.
Types of Magnetic Materials
- •Diamagnetic: μᵣ < 1, weakly repelled by magnets
- •Paramagnetic: μᵣ > 1 (slightly), weakly attracted
- •Ferromagnetic: μᵣ ≫ 1, strongly magnetic
Mathematical Relationships
B = μH (Magnetic flux density)
μ = μᵣ × μ₀ (Absolute permeability)
χ = μᵣ - 1 (Magnetic susceptibility)
M = χH (Magnetization)
Applications
- •Transformer core design
- •Magnetic shielding
- •Inductor design
- •MRI machine engineering
Superconductors and Perfect Diamagnetism
What are Superconductors?
Superconductors are materials that, when cooled below a critical temperature, exhibit zero electrical resistance and perfect diamagnetism (μᵣ = 0). They completely expel magnetic fields from their interior, a phenomenon known as the Meissner effect.
Levitation Effect
The perfect diamagnetism of superconductors allows for magnetic levitation. A magnet placed above a superconductor will float due to the complete expulsion of magnetic field lines.
Common Superconductors
Mercury: Tc = 4.2 K (-269°C)
First discovered superconductor
YBCO: Tc = 93 K (-180°C)
High-temperature superconductor
Niobium: Tc = 9.3 K (-264°C)
Used in MRI machines