Magnetic Permeability and Relative Permeability (μ, μ_r)
Physics · Magnetism And Matter · NEET
Magnetic permeability (μ) tells you how easily a material lets magnetic field lines pass through it: B = μH. Relative permeability μ_r = μ/μ₀ is just a number (no unit) that compares the material to vacuum, and it links to susceptibility by μ = μ₀μ_r = μ₀(1+χ). Memory hook: "μ_r = how many times better than empty space" — vacuum has μ_r = 1, iron has μ_r in the hundreds or thousands.
Same magnetising field H, but higher permeability μ (larger μ_r) crowds in more field lines, giving a bigger B. Vacuum has μ_r = 1; ferromagnets like iron have μ_r far greater than 1.
Your doubts, answered
What is the difference between permeability μ and relative permeability μ_r?
Permeability μ is the full quantity in B = μH and carries units of T m A⁻¹ (or H m⁻¹). Relative permeability μ_r = μ/μ₀ is only a pure ratio (no unit) that says how many times more permeable the material is than vacuum. So μ has units, μ_r does not.
Does relative permeability have a unit?
No. μ_r is a ratio of two permeabilities (material ÷ vacuum), so all units cancel. It is a plain number. For vacuum μ_r = 1, for most paramagnets μ_r is slightly above 1, and for ferromagnets like iron μ_r can be several hundred to several thousand.
How do I get permeability μ from susceptibility χ?
Use μ = μ₀(1 + χ). First add 1 to χ to get μ_r = 1 + χ, then multiply by μ₀ = 4π × 10⁻⁷ T m A⁻¹. This is the single most tested link in this concept — NEET 2020 asked exactly this for an iron rod.
Why is μ_r about 1 for air but huge for iron?
μ_r = 1 + χ. Air (paramagnetic) has a tiny positive χ, so μ_r ≈ 1. Iron (ferromagnetic) has a very large positive χ (χ >> 1), so it strongly concentrates field lines and μ_r becomes large. Diamagnetic materials have small negative χ, so μ_r is just under 1.
⚠️ The NEET trap ✗ Multiplying only by χ: μ = μ₀ × χ, giving μ = 4π×10⁻⁷ × 599. ✓ Add 1 first: μ = μ₀(1 + χ) = 4π×10⁻⁷ × 600 = 2.4π×10⁻⁴ T m A⁻¹. 🧠 The '+1' is the vacuum's own contribution — never drop it. μ_r = 1 + χ, not χ.
Real NEET questions
2020
An iron rod of susceptibility 599 is subjected to a magnetising field of 1200 A m⁻¹. The permeability of the material of the rod is (μ₀ = 4π × 10⁻⁷ T m A⁻¹):
A · 2.4π × 10⁻⁵ T m A⁻¹
B · 2.4π × 10⁻⁷ T m A⁻¹
C · 2.4π × 10⁻⁴ T m A⁻¹ ✓
D · 8.0 × 10⁻⁵ T m A⁻¹
Solution: Step 1: Use the link between permeability and susceptibility: μ = μ₀(1 + χ). Step 2: Add 1 to χ → μ_r = 1 + 599 = 600. Step 3: Multiply by μ₀: μ = 4π × 10⁻⁷ × 600 = 2400π × 10⁻⁷ T m A⁻¹. Step 4: Write in standard form: 2400 × 10⁻⁷ = 2.4 × 10⁻⁴, so μ = 2.4π × 10⁻⁴ T m A⁻¹. The magnetising field 1200 A m⁻¹ is extra data not needed for μ. Answer: C.
Solved Magnetism And Matter NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Tesla metre per ampere (T m A⁻¹), which is the same as henry per metre (H m⁻¹). Relative permeability μ_r has no unit.
What is the value of μ₀?
μ₀ = 4π × 10⁻⁷ T m A⁻¹ ≈ 1.257 × 10⁻⁶ T m A⁻¹. It is the permeability of free space (vacuum), and its μ_r is exactly 1.
What is the formula linking μ, μ_r and χ?
μ = μ₀μ_r = μ₀(1 + χ). Equivalently μ_r = 1 + χ. This is the key NEET formula for this concept.
Is relative permeability always greater than 1?
No. Paramagnetic and ferromagnetic materials have μ_r > 1. Diamagnetic materials have χ slightly negative, so μ_r is slightly less than 1.
How is permeability related to B and H?
B = μH inside a material, and in vacuum B = μ₀H. Dividing gives μ_r = μ/μ₀, so a higher μ means the material produces a larger B for the same magnetising field H.
