A toroidal magnetic core of mean circumference and uniform cross-sectional area A is wound with N turns of a tightly coupled winding carrying current I. The core material is linear up to saturation, with relative permeability, beyond which the flux density cannot exceed.

Assume fringing and leakage flux are negligible, and that the magnetic field is uniformly distributed within the core. Under these conditions, determine the critical value of current (i.e., the maximum permissible excitation current Iₘₐₓ) at which the flux density in the core just attains.