Simulation · Physics · Class 12

What a core does to a solenoid

From the lesson Magnetisation and magnetic intensity in Magnetism and Matter. Change the values and watch what happens.

The idea behind it

NCERT §5.4

Orbiting electrons give atoms magnetic moments, and in bulk matter these add as vectors. The magnetisation M of a sample is its net magnetic moment per unit volume, M = m_net/V: a vector with dimensions L⁻¹ A, measured in A m⁻¹.
In an empty long solenoid B₀ = μ₀nI. Filling it with a magnetised material adds a field B_m = μ₀M, so B = B₀ + B_m.
The magnetic intensity is defined as H = B/μ₀ − M, also in A m⁻¹. Then B = μ₀(H + M): H stands for the external cause (in a solenoid H = nI, whatever the core), M for the material's response.
For most materials M is proportional to H: M = χH, where the magnetic susceptibility χ is dimensionless. χ is small and positive for paramagnetic materials, small and negative for diamagnetic ones (M opposite to H).
So B = μ₀(1 + χ)H = μ₀μᵣH = μH, with relative permeability μᵣ = 1 + χ (the magnetic twin of the dielectric constant) and permeability μ = μ₀μᵣ, in the same units as μ₀.
χ, μᵣ and μ are linked, so knowing any one gives the other two.
Example 5.5: a core of μᵣ = 400 in windings of 1000 turns per metre carrying 2 A gives H = nI = 2 × 10³ A/m, B = μᵣμ₀H = 1.0 T, and M = (μᵣ − 1)H = 399H ≈ 8 × 10⁵ A/m.
Example 5.5: the magnetising current is the extra current that would give the same B with no core, from B = μ₀n(I + I_M); it comes to I_M = 794 A, showing how much the core adds.

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