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Question

A material with susceptibility \( \chi = 2 \times 10^{-3} \) has a relative permeability \( \mu_r \)
of:

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Explanation

**Relation between B, H, M** is B = μ₀(H+M) = μ₀(1+χ)H. Susceptibility χ = μ_r -1 quantifies material response. Given B, μ_r, n, current I = B/(μ₀ μ_r n), with μ₀ = 4π×10⁻⁷ T·m/A, enabling current calculation for desired B with magnetic core. μ_r = 1 + chi . Given: chi = 2 × 10⁻³ . Substitute: μ_r = 1 + 2 × 10⁻³ = 1.002 . Substituting values gives 1.002, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.

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