A toroid wound with 100 turns per metre of wire carries a current of 3 A. The core of the toroid is made of iron having relative magnetic permeability μᵣ=5000 under the given conditions. The magnetic field inside the iron is . (μ₀=4π×10⁻⁷ T m A⁻¹)

Question

Accepted Answer

(4) 1.88 T. Given: n=100 turns per metre, I=3 A, μᵣ=5000, μ₀=4π×10⁻⁷ T m A⁻¹. Idea: inside a toroid the magnetising field is H=nI (Ampere's circuital law), and the iron core multiplies the field by its relative permeability: B=μ₀μᵣ H. H=nI=100×3=300 A m⁻¹. μᵣ H=5000×300=1.5×10⁶ A m⁻¹. B=4π×10⁻⁷×1.5×10⁶=1.88 T - a field the winding alone could never produce, which is what a ferromagnetic core is for.

A toroid wound with 100 turns per metre of wire carries a current of 3 A. The core of the toroid is made of iron having relative magnetic permeability μᵣ=5000 under the given conditions. The magnetic field inside the iron is ______. (μ₀=4π×10⁻⁷ T m A⁻¹)

Step-by-step solution

Why the other options are wrong