Electromagnetism, Steam from Ramen?

Takeshi Kinoshita (Associate Professor, Department of Electronics and Electrical Engineering)

Electromagnetism is considered a prime example of a disliked university lecture course. However, everyone knows its importance, and it remains a required course in the Faculty of Science and Technology. Here, I would like to share some honest thoughts that are not usually mentioned in electromagnetism textbooks or lectures. In fact, you can sometimes see from textbooks that even those who teach it have a lot of confusion and struggles.

The most common reason for disliking electromagnetism is, "I don't understand it because I can't see it." Things with the character "ki" (気) in their name (not written with the character for "thing," 物) are all formless, such as "kiai" (fighting spirit), "genki" (energy), "fun'iki" (atmosphere), and "kitai" (gas). For example, the concepts of "kai" (界) or "ba" (場) in terms like "denkai" or "denba" (electric field) are abstract and can even feel connected to ideas like "god," "dominion," or "fate." While the direct purpose of studying electromagnetism is to learn how to elucidate and utilize invisible phenomena, which is the essence of civilization, another important reason it is a required course seems to be for "mental imagery training." In addition to things that are invisible but measurable, like electric current and voltage, electromagnetism introduces things that do not exist and therefore cannot be measured, making it perhaps a "ghost world." The latter, in particular, are difficult to understand and include concepts that have been the subject of debate as to whether they are real or correct.

Everyone knows about "magnetic lines of force," a term also used as a metaphor for "charm" or "attractive force." Many people have experienced seeing the patterns of these lines by using iron filings with a magnet, which has N and S magnetic poles. However, the source of these magnetic lines of force is questionable. Textbooks state that there are "magnetic charges" at the magnetic poles, but this is often accompanied by a note saying they "do not actually exist," or with an explanation that is critical of this idea. This must be confusing for students. On the other hand, "electric charges," like electrons and ions, are the source of the lesser-known "electric lines of force," and this concept is straightforward. Science allows us to invent and use non-existent things if they are useful for a correct understanding. So, do we use "ghosts" too? Numbers themselves have no shape, and "imaginary numbers" (kyosū) are useful "lie numbers" (usosū, a pun). Come to think of it, laws and currency also have no true form.

When you move a metal rod across the magnetic lines of force of a bar magnet, electricity is generated in the rod. This is called "electromagnetic induction" and is the principle of power generation. It is an important topic in electromagnetism, and the term aptly describes the phenomenon. Now for a strange question: conversely, if you rotate a cylindrical bar magnet around its central axis, will the metal rod generate electricity? If the magnetic lines of force (or more precisely, magnetic flux lines) were "growing" from the magnetic charges like hair, they would rotate with the magnet, and crossing them with the rod would generate electricity, just as before. In fact, no electricity is generated, so we can conclude that they are not "growing" out of it. I explain this using the analogy of "steam from ramen." Some textbooks state that since magnetic charges do not exist in the first place, the lines are not "growing." Since this paradox is rarely encountered in practical applications, many textbooks do not mention it, and many readers—as I once did—misunderstand and think the lines are "growing."

There are other "ghosts" besides this. These range from useful but non-existent concepts that were initially considered heretical, like Maxwell's "displacement current," to things whose existence was difficult to prove, like the "vector potential," and even "tricky" concepts like "magnetic current."

Although "electromagnetism is difficult because it's invisible," if you turn this on its head and view it as a subject for acquiring the skill of creating and using non-existent things through flexible thinking and the power of imagination, I believe there are ways of understanding and learning that are not bound by textbooks and lectures. In fact, I believe that some of you may have a far superior understanding than those who teach it. Are "ghosts" useful friends?