Ohms Law for Magnetic Circuits

Recalling the equation introduced for Ohm's law for electric circuits. $$ \text{Effect} = {\text{cause} \over \text{opposition}} $$ The same equation can be applied for magnetic circuits. For magnetic circuits, the effect desired is the flux $\Phi$. The cause is the magnetomotive force (mmf) , which is the external force (or "pressure") required to set up the magnetic flux lines within the magnetic material. The opposition to the setting up of the flux $\Phi$ is the reluctance $S$. Substituting, we have $$\bbox[10px,border:1px solid grey]{\Phi = {m.m.f \over S}} \tag{1}$$
The magnetomotive force is proportional to the product of the number of turns around the core (in which the flux is to be established) and the current through the turns of wire (Fig. 1).
Defining the components of a magnetomotive
Fig. 1: Defining the components of a magnetomotive force.
In equation form, $$ \bbox[10px,border:1px solid grey]{m.m.f = NI} \, \text{(ampere-turns, At)} \tag{2}$$ This equation clearly indicates that an increase in the number of turns or the current through the wire will result in an increased "pressure" on the system to establish flux lines through the core.
Although there is a great deal of similarity between electric and magnetic circuits, one must continue to realize that the flux $\Phi$ is not a "flow" variable such as current in an electric circuit. Magnetic flux is established in the core through the alteration of the atomic structure of the core due to external pressure and is not a measure of the flow of some charged particles through the core.