A rod with circular cross-section area 2 cm² and length 40 cm is wound uniformly with 400 turns of an insulated wire. If a current of 0.4 A flows in the wire windings, the total magnetic flux produced inside the windings is 4π × 10⁻⁶ Wb. The relative permeability of the rod is (Given: permeability…

Question

A rod with circular cross-section area 2 cm² and length 40 cm is wound uniformly with 400 turns of an insulated wire. If a current of 0.4 A flows in the wire windings, the total magnetic flux produced inside the windings is 4π × 10⁻⁶ Wb. The relative permeability of the rod is (Given: permeability of vacuum μ₀ = 4π × 10⁻⁷ N A⁻²)

Accepted Answer

(3) 5/16. n=(400)/(0.4)=1000 turns per metre, so B=μᵣμ₀nI=μᵣ×4π×10⁻⁷×1000×0.4. Total flux =NBA=400× B×2×10⁻⁴=4π×10⁻⁶ Wb. Solving gives μᵣ=5/(16).

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