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]).
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.
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