The relationship between the magnetic susceptibility (x) and the magnetic permeability (μ) is given by :
( μ₀ is the permeability of free space and μ_T is relative permeability)

Solution

Physics sir · 3 steps

Start from μᵣ = 1 + χ, then write μᵣ as μ/μ₀ and the answer drops out.

1. Two definitions. Magnetisation is M = χ H, and the field inside the material is B = μ₀ (H + M). Put the first into the second.

   B = μ₀ (1 + χ) H = μ H

2. Compare. So μ = μ₀ (1 + χ), which means μᵣ = μ/μ₀ = 1 + χ.
3. So. Rearranging gives χ = μ/μ₀ - 1 = μᵣ - 1, which is option (a).

The idea to keep. Remember μᵣ = 1 + χ. Vacuum has χ = 0 and μᵣ = 1, so use that as a quick check on any formula you write.

Answer from the NTA final answer key. Solution by PrepWiser.