Closed path followed by magnetic flux is called magnetic circuit

Usually consists of magnetic materials having high permeability (e.g., iron, soft steel, etc.).

magnetic flux starts from a point and finishes at the same point after completing its path \[\begin{aligned} \text{Flux density }B & =\dfrac{\phi}{a}~\text{Wb/m\textsuperscript{2}}\\ \text{Magnetising force }H & =\dfrac{B}{\mu_{0}\mu_{r}}\\ & =\dfrac{\phi}{a\mu_{0}\mu_{r}}~\text{AT/m} \end{aligned}\]

\[\begin{aligned} & \rightarrow Hl=NI\\ \Rightarrow & \dfrac{\phi}{a\mu_{0}\mu_{r}}\times l=NI\\ \Rightarrow & \phi=\dfrac{NI}{\left(l/a\mu_{0}\mu_{r}\right)}~\text{Wb} \end{aligned}\]

\[\begin{aligned} & \boxed{\phi =\dfrac{NI}{\left(l/a\mu_{0}\mu_{r}\right)}~\text{Wb}} \end{aligned}\] Conclusion: amount of flux set-up in the core

\(\propto N\) and \(I\) i.e. \(NI\) called magnetomotive force (mmf) \[\Rightarrow \phi ~\text{increases if either of the two increases and vice-versa}\]

inversely \(\propto l/a \mu_0 \mu_r\) called reluctance of the magnetic path \[\begin{aligned} \Rightarrow &\text{Reluctance: opposition offered to}~ \phi~ \text{by the magnetic path} \\ \Rightarrow &\text{lower reluctance higher will be} ~\phi ~\text{and vice-versa} \end{aligned}\]

Therefore, \[\phi = \dfrac{\text{mmf}}{\text{reluctance}}\]

Note: expression strong resemblance to Ohm’s Law for electric current (I=emf/resistance)

referred to Ohm’s law of magnetic circuits

Magnetic field: The region around a magnet where its poles exhibit a force of attraction or repulsion

Magnetic flux (\(\phi\)):

The amount of magnetic lines of force set-up in a magnetic circuit

unit is weber (Wb).

analogous to electric current \(I\) in electric circuit

Magnetic flux density (\(B\)): at a point is the flux per unit area at right angles to the flux at that point \[B=\frac{\phi}{A} \mathrm{~Wb} / \mathrm{m}^{2} \quad \text { or } \quad \mathrm{T}\left(1 \mathrm{~Wb} / \mathrm{m}^{2}=1 \times 10^{4} \mathrm{~Wb} / \mathrm{cm}^{2}\right)\]

Permeability (\(\mu\)): The ability of a material to conduct magnetic lines of force through it

greater the \(\mu\) of a material, the greater is its conductivity for the magnetic lines of force and vice-versa

air or vacuum is the poorest represented \(\mu_0=4\pi\times10^{-7}\) H/m

Relative permeability (\(\mu_r\)): The absolute (or actual) permeability of a magnetic material is much greater than \(\mu_0\).

\(\mu_r\) of a magnetic material is given in comparison with air or vacuum \[\mu_{r}=\frac{\mu}{\mu_{0}} \quad \text { or } \quad \mu=\mu_{0} \mu_{r}\]

Obviously, \(\mu_r\) of air would be 1.

\(\mu_r\) of all the non-magnetic materials is also 1.

However, its value is as high as 8000 for soft iron, whereas, its value for mumetal (iron 22% and nickel 78%) is as high as 1,20,000.

Magnetic field intensity (\(H\)): The force acting on a unit north pole (1 Wb) when placed at a point in the magnetic field \[H=\frac{\mathrm{m} \cdot \mathrm{m} \cdot \mathrm{f}}{\text { length of magnetic path }}=\frac{N I}{l} \mathrm{AT} / \mathrm{m}\]

Magneto-motive force (mmf): The magnetic pressure which sets-up or tends to set-up magnetic flux in a magnetic circuit

As per work law it may be defined as: The work done in moving a unit magnetic pole (1 Wb) once round the magnetic circuit \[\text{mmf} = NI ~\text{ampere-turns (AT)}\]

analogous to emf in an electric circuit

Reluctance (\(S\)): The opposition offered to the magnetic flux by a magnetic circuit \[\text { Reluctance, } S=\frac{l}{a \mu_{0} \mu_{r}}\]

analogous to resistance in an electric circuit

Permeance: It is a measure of the ease with which flux can be set-up in the material.

It is just reciprocal of reluctance of the material \[\text { Permeance }=\frac{1}{\text { reluctance }}=\frac{a \mu_{0} \mu_{r}}{l} \text { Wb/AT or } \mathrm{H}\]

analogous to conductance in an electric circuit

Reluctivity: It is specific reluctance and analogous to resistivity in electric circuit