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4. The application of Ampère's theorem - emphasizing the magnetic circuit

Lecture's plan

Introduction

  1. The importance of the magnetic circuit notion
  2. An example of magnetic circuit
  3. Defining the integration contour for the application of Ampère's theorem
  4. The application of Ampère's theorem - emphasizing the magnetic circuit
  5. Hopkinson's law
  6. Analogy between magnetic circuits/electrical circuits
  7. Application for modelling an electromechanical converter
  8. Defining the equivalent magnetic circuit
  9. The reduction of the equivalent magnetic circuit
  10. Flux-current relation
  11. The calculus of the magnetic co-energy and attraction force

Due to the symmetry, on the chosen integration contours, the induction field produced by / current that flows through the reel is always tangential at contour and has constant amplitude. The result is:

  • If the contour has the radius R1 smaller than Ri (the internal radial of the annular core) - the G1 contour from figure 2) 1:
    		(1)
  • If the contour has the radius R2 bigger than Ri but smaller than Re (the external radius of the annular core) the G2 contour from figure 2):
    		(2)
  • finally, if the contour has the R3 bigger than Re - the G3 contour from figure 2):
    		(3)

where m0 represents the magnetic permeability of the vacuum and of the air, and m represents the magnetic permeability of the material from which the annular core is made.

It is ascertained that in any point outside the torus, the field is null. The entire flux induced by the current, circulates, therefore, within this volume, similar to an electrical circuit in which the power only flows through conductors. By analogy, we can define torus as being a magnetic circuit.

1 actually,for any contour situated in a plan which does intersect the reel.

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Last update: 2005, September, 30 | Translation: Sergiu Ivanov | Realization: Florin Ravigan, Cristian Vladu