An iron ring of relative permeability μ_r has windings of insulated copper wire of n turns per metre. When the current in the windings is I, find the expression for the magnetic field in the ring.

Solution

There will be two magnetic field one due to current and another due to magnetics.

$B = B_{0} + B_{m} B = μ_{0} nI + μ_{0} M B = μ_{0} H + μ_{0} χH B = μ_{0} (1 + χ) H B = μ_{0} μ_{r} H$

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