Flux-cutting and Electromotive Force: How to Motivate Students into Electrodynamics

A. SihvolaDepartment of Radio Science and Engineering

Aalto University School of Electrical Engineering, Espoo, Finland

Abstract— Efforts in teaching electromagnetics culminate often in attempts to cover Maxwell equations. A challenging task indeed, it requires several stages of focus on varying aspects and character of electric and magnetic fields. The divergence laws (electric and magnetic), Coulomb/Gauss relations, which talk about static field effects of sources and the flow of fluxes, can be visualized with some success on blackboard or computer screen with lines, arrows, and colors, although vector fields (especially in three dimensions) do not easily transform into flat images. However, trying to transmit the meaning of the dynamic equations (generalized Ampre’s law and the Faraday law) require a considerably larger amount of efforts. In this presentation, I try to discuss ways of classroom behavior which I personally feel most efficient and rewarding from the viewpoint of an electromagnetics teacher. Some of the methods that I use have also been described in my earlier articles [1].

Forum for Electromagnetic Research Methods and Application Technologies (FERMAT)

Faraday’s law:y

Differential form ∂Bt∂

∂−=×∇

BE

Stokes’s law

∫∫ ⋅=⋅×∇ cFSF dd

f

∫∫ ⋅=⋅×∇ cFSF dd

Macroscopic form

Φ∂t∂Φ∂

−=EMF

Textbook research: three approaches into introducing Faraday’s law

• starting point: full Maxwell equationsK C lli H J– Kong, Collin, Haus, Jones,…

• electrostatics→ (static currents)→  magnetostatics→ Faraday’s law→ Ampère−Maxwell law– Cheng, Pollack−Stump, Kraus, Jackson,…

• statics→ slowly‐varying (quasi‐static) fields→statics→ slowly varying (quasi static) fields→ dynamics

Notaroš Reit Milford Christie Popo ić Popo ić– Notaroš, Reitz−Milford−Christie, Popović−Popović,…

∂∇

BEt∂

−=×∇ Et∂

Colorful law of Faraday:Colorful law of Faraday:Aalto/ELEC students: March 7, 2014

586206450 0645.0=g

gain=g

39 43 pre% 100pre% post %

−−

=

Effect of discussionEffect of discussion

Confidencedefinitely correct: 2 probably correct: 1 just guessing: 0

• Before discussion: confidence 1,109

• After discussion: 1 337After discussion: 1,337

• Trends in different categories:

AGAIN: The colorful law of Faraday:AGAIN: The colorful law of Faraday:DELTA doctoral students: May 15,2014

21251600 160.0=g

12 16

Effect of discussionEffect of discussion

Confidencedefinitely correct: 2 probably correct: 1 just guessing: 0

• Before discussion: confidence 1.000

• After discussion: 1.054

Conclusions?Conclusions?

• Faraday’s law is tricky!

• Correlation between electomagnetics• Correlation between electomagnetics education and understanding Faraday’s law:– negative?

• But: learning from discussionBut: learning from discussion– positive!

A. Sihvola, J. Leppävirta, H. Kettunen: Signs, curls, and time variations: learning to appreciate Faraday’s law. Advanced Electromagnetics, 1(1), May 2012