Magnetic Circuits

Composition

Made of:

• magnetic core
• N turns of wire carrying current

Magnetomotive Force

$F=NI$ where the units are [Ampere*turn]

Ohms Law for EMF

$E_{mf}=RI$
For an electric circuit:
$R=\frac{1}{\sigma }\frac{L}{A}$
For a magnetic circuit:

$mmf=NI=R_{eluctance}\cdot \varphi$
Where reluctance is in: $R=\frac{A\cdot turn}{Wb}$ $R=\frac{l}{{\mu }_{permeability}{A}_{cross}}$
Which is better represented as
$R=\frac{l}{\mu A}=\frac{l}{{\mu }_0{\mu }_{R}A}$
Where ${\mu }_0$ = $4\pi \cdot 10^{-7}\frac{H}{m}$

Permeability

Permeability is basically the conductivity for flux

Good magnetic materials have high permeability

The Big Magnetic Daddy of Equations

$F=NI=R\varphi =Hl$ Where you can rearrange, and sub new variables into this equality and solve for what you need.
You can derive
$B=\mu H$ Which shows the relationship of B and H, notably, for a highly permeable magnetic material, a small H causes a large change in B.

Core Magnetization

See Core Magnetization

Sub Concepts

Flux Leakage

Some of the flux produced stays outside the core so you need a larger mmf to establish a desired flux.

Fringing Effect

If there is an air gap in a core, the flow lines of the magnetic forces (flux) are larger than the cross sectional area of the core

Magnetic Circuit Analysis

See Magnetic Circuit Analysis