Demonstrative Video
Magnetic Circuit and its Analysis
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
Important terms in magnetism
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