Answers and Discussions for
Problem 1
Create and Solve Magnetic Equivalent Circuit
A magnetic equivalent circuit (MEC) needs to be constructed from the given UU core inductor geometry. A magnetomotive force with general form $ \mathcal{F} = Ni $ acts as an analogue of an independent voltage source. In general, a reluctance may be expressed as $ \mathcal{R} = \frac{\ell}{\mu A} $ and function as a resistance analogue. If the steel has high permeability, then the reluctance associated with a path through steel is small (real conductor equivalent). In this problem, the permeability of air (linear, isotropic, and homogeneous) is treated as free space: $ \mu_{\text{air}} = \mu_{r,\text{air}} \mu_0 \approx \mu_0 $. Without any fringing or leakage considered, magnetic flux $ \Phi $ will more or less follow the direction of the steel.
