Sandro Ronca

Physics and Mathematics of the Rotating Magnetic Field

From AC motors to waves and harmonics — an e-book that students learn from by experimenting with 14 interactive cards.

Cover of Physics and Mathematics of the Rotating Magnetic Field

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These are two of the interactive cards from the book, exactly as students use them while reading. Start the animation, tick the boxes, move the sliders. They work on desktop, tablet and phone, with no installation.

Interactive card 2.1 — A two-pole synchronous motor: the three-phase currents, the field of each phase, their sum and the rotating poles. Tick Description to see the parts of the machine.

Interactive card 7.1 — A small function plotter: write a function of x and t with the keypad, press PLOT and start the time. Can you find a wave that travels without changing shape? Then measure its phase velocity and wavelength with the stopwatch.

More cards in action

The three-phase system (card 2.1-A): how the EMFs are generated, star and delta connections of generator and load, phase and line currents. Then the induction motor (card 3.1): slip, rotor currents and torque appear as the load is applied.

Inside the book

Every chapter is built around cards like these. Each one comes with the text that explains what to look at and why.

Card 3.1, induction motor
Card 3.1 · Induction motorSquirrel-cage rotor, slip, torque and reaction currents.
Card 4.2, distributed winding
Card 4.2 · Distributed windingsThe air-gap field built up with the circulation law.
Card 5.1, four-pole machine
Card 5.1 · Isotropic machineField lines, rotating poles and the air-gap distribution.
Card 6.2, Leblanc's theorem
Card 6.2 · Leblanc’s theoremThe rotating field as a sum of counter-rotating fields.
Card 2.2, four-pole field
Card 2.2 · Four-pole fieldWhy the field rotates at half the speed, phase by phase.
Card 7.3, spatial harmonics
Card 7.3 · Spatial harmonicsFundamental, 3rd and 5th harmonics of the rotating field.

Contents

  • Part One
  • 1 – The Discovery of the Rotating Magnetic Field
  • 2 – The Rotating Magnetic Field: A First Look
  • 3 – The Induction or Asynchronous Motor
  • Part Two
  • 4 – Magnetic Field in the Air Gap of Isotropic Machines
  • 5 – The Rotating Magnetic Field in an Isotropic Machine
  • 6 – Counter-Rotating Fields and Leblanc’s Theorem
  • Part Three
  • 7 – The Mathematics of Rotating Fields
  • Appendix: Derivation of the Torque Formula of an Induction Motor

Who it is for

Courses on electrical machines, electromechanical energy conversion, AC circuits and applied electromagnetism, from first encounters with the rotating field to the mathematics of traveling waves and spatial harmonics.

The cards can be shown in class on a projector, assigned as guided exploration, or simply left to curious students. The prerequisites are basic AC circuits and trigonometry; the book recalls what is needed.

Download the free sample (EPUB) — the introduction and the first two chapters.

Reading the e-book with live cards

The cards run inside the e-book in readers that support scripts. On a computer we recommend one of these free readers; on iPad, iPhone and Mac, Apple Books works too. In other readers each card appears as a picture with a link that opens it in the browser.

Complimentary copy for instructors

If you teach a related course and would like to evaluate the book, I will gladly send you the complete e-book. Please write from your institutional address and mention your course.