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5. Hopkinson's Law

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

If Ri şi Re have similar values (meaning that the whirls are smaller than the medium radius Rm = (Ri+Re)/2), we can consider, without risking major errors, that all the integration contours situated within the torus have the approximately same Rmlenght.

From here - the magnetic induction is constant in any point of a right section of the torus. As induction is, in any point, perpendicularly to the right section (because it is tangential to the in tegration contour), the y flux through a right sectoin of the torus can be approximated:
(4)
where S is the right section of the torus.

Combining equations (2) and (4) the result will be

(5)
with = 2.p.Rm

By noting and defining:

  • F = N.I magnetomotive force expressed in ampere-turns;
  • R = ml.S, reluctance of the magnetic circuit,

thus (5) could be write in this form:
(6)
This ecuation is also known as The Hopkinson's Law

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