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μ₀ is the permeability of vacuum and χₘ is the magnetic susceptibility of a material. Then the permeability of the material is

Asked in GUJCET 2017 · Magnetisation, intensity and susceptibility

• (1) μ=μ₀+χₘ
• (2) μ=μ₀(χₘ-1)
• (3) μ=μ₀(1-χₘ)
• (4) μ=μ₀(1+χₘ)

Step-by-step solution

Why the other options are wrong

• (1) Adds a pure number to a quantity that has units: χₘ is dimensionless while μ₀ is in T m A⁻¹, so the sum is not a permeability at all.
• (2) For vacuum χₘ=0, and this expression then gives μ=-μ₀ instead of μ₀. For every ordinary material χₘ1, so it would make the permeability negative.
• (3) The sign is the wrong way round: it would give μ<μ₀ for a paramagnet (χₘ>0) and μ>μ₀ for a diamagnet (χₘ<0), the opposite of how these materials behave.

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