Magnetizing Force

The magnetomotive force per unit length is called the magnetizing force (H). In equation form, $$\bbox[10px,border:1px solid grey]{H = {m.m.f \over l}} \, \text{(At/m)}\tag{1}$$ Substituting for the magnetomotive force will result in $$\bbox[10px,border:1px solid grey]{H = {NI \over l}} \, \text{(At/m)}\tag{2}$$
For the magnetic circuit of Fig. 1, if $NI = 40 \,At$ and $l = 0.2\, m$, then $$H = {NI \over l} = {40 \ over 0.2} = 200 \, \text{At/m}$$
Defining the magnetizing force of a magnetic circuit.
Fig. 1: Defining the magnetizing force of a magnetic circuit .
In words, the result indicates that there are $200 \,At$ of "pressure" per meter to establish flux in the core.
Note in Fig. 1 that the direction of the flux $\Phi$ can be determined by placing the fingers of the right hand in the direction of current around the core and noting the direction of the thumb. It is interesting to realize that the magnetizing force is independent of the type of core material-it is determined solely by the number of turns, the current, and the length of the core.
The applied magnetizing force has a pronounced effect on the resulting permeability of a magnetic material. As the magnetizing force increases, the permeability rises to a maximum and then drops to a minimum, as shown in Fig. 2 for three commonly employed magnetic materials.
The flux density and the magnetizing force are related by the following equation: $$\bbox[10px,border:1px solid grey]{B = \mu H} \tag{3}$$
Defining the magnetizing force of a magnetic circuit.
Fig. 2: Variation of $\mu$ with the magnetizing force.
Equation (3) can be derived as $$ \begin{split} H &= {mmf \over l} \\ &= {NI \over l} = {\Phi R \over l} ; \text{where} R = {l \over \mu A}\\ &= {\Phi ({l \over \mu A}) \over l}= {\Phi l \over \mu A l}\\ &= {\Phi \over A} {1 \over \mu }\\ H&= {B \over \mu }\\ B&= \mu H \end{split}$$ This equation indicates that for a particular magnetizing force, the greater the permeability, the greater will be the induced flux density. Since henries (H) and the magnetizing force (H) use the same capital letter, it must be pointed out that all units of measurement in the pages, such as henries, use roman letters, such as H, whereas variables such as the magnetizing force use italic letters, such as H.