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 windings is 4π × 10⁻⁶ Wb. The relative permeability of the rod is: [μ₀ = 4π × 10⁻⁷ N A⁻²]
Options

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 windings is 4π × 10⁻⁶ Wb. The relative permeability of the rod is: [μ₀ = 4π × 10⁻⁷ N A⁻²]

Options

G1 Physics · Accepted Answer

For a solenoid, B = μ(r)μ₀(N/l)I and flux Φ = BA. Thus μ(r) = Φl/[μ₀NIA]. Substituting Φ = 4π×10⁻⁶ Wb, l = 0.4 m, N = 400, I = 0.4 A and A = 2×10⁻⁴ m² gives μ(r)=125.