Electrical Machines · Fundamentals

Magnetic Circuits: Core Concepts and Analysis

Dr. Mithun Mondal BITS Pilani, Hyderabad Campus Electrical Machines

Demonstrative Video

SECTION 01

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.).

  • \[\begin{aligned} \text{Flux density }B & =\dfrac{\phi}{a}~\text{Wb/m\textsuperscript{2}}\\ \text{Magnetising force }H & =\dfrac{B}{\mu_{0}\mu_{r}}\\ & =\dfrac{\phi}{a\mu_{0}\mu_{r}}~\text{AT/m} \end{aligned}\]
    magnetic flux starts from a point and finishes at the same point after completing its path
\[\begin{aligned} & \rightarrow Hl=NI\\ \Rightarrow & \dfrac{\phi}{a\mu_{0}\mu_{r}}\times l=NI\\ \Rightarrow & \phi=\dfrac{NI}{\left(l/a\mu_{0}\mu_{r}\right)}~\text{Wb} \end{aligned}\]
Key Concepts
\[\begin{aligned} & \boxed{\phi =\dfrac{NI}{\left(l/a\mu_{0}\mu_{r}\right)}~\text{Wb}} \end{aligned}\]
  • \[\Rightarrow \phi ~\text{increases if either of the two increases and vice-versa}\]
    magnetomotive force (mmf)\(NI\)\(I\)\(\propto N\)
  • \[\begin{aligned} \Rightarrow &\text{Reluctance: opposition offered to}~ \phi~ \text{by the magnetic path} \\ \Rightarrow &\text{lower reluctance higher will be} ~\phi ~\text{and vice-versa} \end{aligned}\]
    of the magnetic path called inversely
  • \[\phi = \dfrac{\text{mmf}}{\text{reluctance}}\]
    Therefore,

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

  • referred to Ohm’s law of magnetic circuits

SECTION 02

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

  • \[B=\frac{\phi}{A} \mathrm{~Wb} / \mathrm{m}^{2} \quad \text { or } \quad \mathrm{T}\left(1 \mathrm{~Wb} / \mathrm{m}^{2}=1 \times 10^{4} \mathrm{~Wb} / \mathrm{cm}^{2}\right)\]
    Magnetic flux density (\(B\)):
Key Concepts
Key Concepts
  • \[H=\frac{\mathrm{m} \cdot \mathrm{m} \cdot \mathrm{f}}{\text { length of magnetic path }}=\frac{N I}{l} \mathrm{AT} / \mathrm{m}\]
    Magnetic field intensity (\(H\)):
analogous to resistance in an electric circuit
  • \[\text { Reluctance, } S=\frac{l}{a \mu_{0} \mu_{r}}\]
    Reluctance (\(S\)):

    • analogous to resistance in an electric circuit

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