Mad Teddy's introduction to electromagnetism

Mad Teddy's web-pages

Electromagnetism - an introduction

When I began this website in early 2005, it wasn't my intention to have a page devoted to "electromagnetic theory". I wanted the "Electrical stuff" pages to have a strong "hands-on" feel to them, just like those wonderful old books to which I keep referring.

However, as I produced more and more electrically-oriented material, I found that I kept needing to mention some aspect of electromagnetism. I'd intended to make brief explanatory comments as I went; but I found that the resulting comments were anything but brief and were making the pages into which they were inserted long, messy, and tedious - the exact opposite of what I wanted. Furthermore, I found that I was going to have to repeat myself over and over again.

So, reluctantly, I eventually decided to "bite the bullet" and include this page. I've tried to keep it as simple as possible. If you already know a fair bit about electromagnetism, you can always skip it and continue to the more obviously practical pages. If you do decide to read on, I hope you find this page interesting - and there's nothing to stop you trying the experiments described herein yourself, if you choose!

In 1820 (some authors say 1819), the Danish physicist Hans Christian Oersted (1777-1851) performed a simple experiment. He arranged a piece of wire above a compass needle and passed an electric current through the wire.

The compass needle was deflected. It ended up pointing not, as you might expect, parallel to the wire, or even directly at it - but at right-angles to it.

When Oersted reversed the current, the needle settled down pointing in the opposite direction.

When the experiment was repeated with the wire was below the needle, instead of above it, the needle would deflect as before - but this time, pointing in the opposite direction in each case.

This seems to suggest that something which may be called a "magnetic field" forms around the wire when a current flows in it. Further experiments can verify this.

If the wire is positioned vertically, and the compass is moved around it while current is flowing, the needle will always position itself pointing skew to the wire, rather than parallel to it or with one of its ends pointing toward the wire. If the battery positive is connected to the top end of the wire, and the negative to the bottom end, the north pole of the needle will point clockwise with respect to the wire when seen from above - and it will point anticlockwise if the battery connections are reversed.

If some iron filings are sprinkled on the card (in an arrangement like that shown above) near to the wire, the current switched on and the card tapped to reduce friction between the filings and the card, the filings will form a pattern of concentric circles, again showing the circular nature of the magnetic field.

Certainly, these are very simple experiments - but with profound implications. If it weren't for this electromagnetic effect, the modern technological world as we know it simply couldn't exist. Put it this way: you wouldn't be reading this on your computer screen right now. There wouldn't even be any computers!

Just think for a moment what the implications are. (Even if you're an "old hand" with this stuff, the following may help you to see it all in a fresh light.)

Firstly, there's a distinctly three-dimensional aspect to this. It's almost essential to show these effects in some sort of perspective view, like in the diagrams above, in order to convey a sense of what is going on. That's unusual; many physical laws can be illustrated adequately using two-dimensional, or "flat", diagrams.

Secondly, and even more importantly, the whole phenomenon is asymmetrical. The direction of the magnetic field depends on the direction of the current. If these directions were parallel (i.e. in the same dimension), it wouldn't be such a big deal - but that's not the case! The direction of the current in one dimension determines the direction of the magnetic field in another dimension. This is an example of chirality, or "handedness", inherent in the structure of the physical world.

So far, I've followed pretty much the usual line taken by most physics textbooks on this subject. The next thing they do, usually, is to consider what happens if the wire is bent into a loop. Almost immediately thereafter, the ultimately confusing term "magnetic lines of force" is introduced; this concept is then extended to deal with what happens with a coil (or solenoid). Not long after that, depending on the textbook's intended audience, the concept is either allowed to "fizzle out" as a major issue, or is tackled by invoking high-powered mathematical tools such as vector calculus (in Maxwell's equations) - so that the implications of what started from a very simple empirical observation (Oersted's experiment) become cloaked in a maze of difficult-to-understand abstraction. How can it get so complicated, so quickly?

Please - don't get me wrong on this. I'm not pouring scorn on vector calculus - far from it; it's a powerful and essential tool in many areas. (Maxwell's contribution was of enormous importance.) My point is that it is difficult, and it is abstract; and that it should be possible to present an account of these observed effects which can be reasonably understood by the lay-person without going to that extreme.

Might it be that the concept of "magnetic lines of force" is more a hindrance than a help? In fact, I'll stick my neck right out:

Might it be that the very idea of "magnetic lines of force" is in fact totally wrong?

You've probably gathered that I've got a serious issue with this. If you'd like to read more on the topic, click here . If you'd rather not, that's okay - it's not necessary to do so in order to get something out of the following pages. You can just continue with this page for my own development of basic electromagnetic ideas; and you can always return to the matter later if you become interested.

From comments I've read on other web-pages, I've discovered that I'm far from the only person in the world who finds the usual "lines of force" discussion ultimately confusing and unconvincing. So, I feel that I'm in good company by taking a different tack. My intention in this page is to sidestep the difficult issues in order to get to a point where we have enough of an idea of what happens so that a simple discussion of practical projects becomes possible, without causing any of us a headache. (The link just given contains my somewhat maverick attempt to deal with the tricky stuff. As mentioned, you can always have a look at it later.)

On the face of it, a circular magnetic field around a piece of wire doesn't look particularly useful. After all, ordinary magnets have two "ends", or poles: a north pole and a south pole. How can we build on Oersted's work to develop something like that?

As a first step, suppose we use a flat, wide strip of metal (a knife, for example) as our conductor, rather than a piece of thin wire. We cut a slot in a piece of card, run the strip though it vertically, connect a battery to its ends, and track the magnetic field with a compass, as before. What happens?

The magnetic field is still there; but now its cross-section (in the plane of the card) is somewhat "sausage-shaped" (dare we say "cigar-shaped" ?), rather than circular.

Now, suppose we have two such strips, inserted through two parallel slots a short distance apart. Above the card, we connect the battery negative to one strip, and the battery positive to the other; below the card, we connect the strips together:

For the moment, let's ignore what's happening between the strips, and compare the effect around the outside of the strips to what happens if we move a compass around a simple bar magnet:

Now, I know that this is perhaps somewhat of a simplification of what you would really see. You'd expect the needles of the compasses located centrally on the upper and lower sides of the magnet to point horizontally, as shown; but it's unlikely that any of the other compass needles would point exactly horizontally or vertically, as suggested here. However, I submit that this diagram represents a reasonable approximation to a real situation - good enough to make the point that the magnetic field around the two strips, where they pass through the card in the previous diagram, is very similar to that around a bar magnet.

Let's return to the two strips. Suppose that each of them is cut lengthwise into thinner strips which are laid out parallel to each other like the original wide strip, with their ends connected together. (Equivalently, you can consider that the original strips have had narrow lengthwise slits cut in them, not quite reaching their ends.)

If the experiment with the compass is repeated, we'll still get essentially the same result. The small gaps will not make any significant difference; the compass needle will - with possible very small variations near the slits - point in the same general direction as before at corresponding points.

It's a small step from here to replace the strips with a coil made up of a single very thin strip. In fact, we can use a long piece of insulated wire. The current along each turn of the coil (or solenoid) will tend to reinforce the same overall pattern as with the original strips.

If a rod of iron or some other "ferromagnetic" material is brought near to the solenoid, the magnetic field concentrated inside the solenoid will tend to draw the rod in. (This is exactly the principle of operation of my two solenoid motors, presented in later pages in this website.)

If the coil is wound onto a rod of ferromagnetic material as a permanent feature, the entire thing becomes an electric magnet, or electromagnet. If it's operating on direct current (DC), it behaves very much like a permanent magnet. If the current in the coil varies in some way over time, things get very interesting and useful. Such coils form the basis for such "moving-coil" devices as electrical meters, loudspeakers, and simple electric motors.

Note that this whole discussion has relied only on observations like those in Dr. Oersted's original experiment with a compass needle. The concept of a magnetic field has been used, rather carefully - but at no point has it been necessary to invoke the troublesome notion of "lines of force".

This link is worth a look - a cheeky and slightly different take on my basic theme.

Also, before going further, I invite you to click on this link to fill in a little more detail about how Oersted made his discovery - and also to get some idea of how Ampère's important observations fit into the story.

It's rather alarming, isn't it - Oersted's discovery of the electromagnetic effect was accidental, or serendipidous. If he hadn't happened to have a compass needle on the bench, and hadn't happened to see it twitch, we might all still be living in the horse-and-buggy era and lighting our houses with candles!

So far, we've considered how an electric current can produce a magnetic field. Next, it's necessary to consider the other side of the coin: how a magnetic field can give rise to an electric current.

Now, I'm going to ask you to do me a favour:

I've found some rather good websites which do a really good job of explaining electromagnetic induction - certainly at least as good as anything I could do. To save this page from unnecessarily blowing out into a monster, would you mind clicking on these links to get the most important parts of the story?

Also, if you ever happen to notice that any of these links no longer works, perhaps you could contact me so that I can take appropriate action and effect a repair job to this page.


In 1831, English scientist Michael Faraday (1791-1867) performed a series of experiments which showed that under certain conditions, an electric current could be generated using a magnet and a coil of wire.

By this time, as a result of Oersted's work, it became possible for simple electric meters called galvanometers to be made. André-Marie Ampère (1775-1836), after whom the unit of electric current is named, is credited with the invention of the first one in 1824. Faraday's experiments involved a galvanometer, a magnet, and coils of wire.

That last link mentions how it's possible to arrange two loops of wire so that a current in one will induce a current in the other. This is the basic principle of a transformer. Faraday made some primitive transformers with which he was able to show electromagnetic induction without the need to physically move anything.

Here is a good link which discusses, fairly simply, the basic principle of a transformer. There is a bit of algebra; if you're the sort of person who finds that confusing, don't worry - the main idea is that (allowing for some inevitable losses due mainly to heating) the voltage induced in the secondary winding will be equal to the voltage across the primary winding times the "turns ratio" - the number of turns in the secondary divided by the number of turns in the primary. If the voltage is thus increased, the current will decrease in the same proportion; and vice versa. Since power equals voltage times current, the power will stay the same (again, allowing for some losses).

(While you're there, have a look at some of the other links within the page - in particular the "solenoid magnetic field" link.)

Okay - the third of those last five excellent links mentions something called Lenz's Law. We need to take a more careful look at this, because it has relevance for some of my projects described in later pages. Have a look at this web-page to see a very simple introduction to Lenz's Law.

Heinrich Friedrich Emil Lenz (1804-1865) was the first person to realize that

"the induced current is such as to oppose the change in the applied field."

What this means is that, if you insert a magnet into a solenoid, thus producing a current in the windings, that current creates a magnetic field of its own which acts in the opposite direction to the magnet's field.

A similar principle applies to electromagnets and transformers. When you switch on an electromagnet, initially there is a fairly heavy current. The magnetic field builds up over a short time (it's not instantaneous); and as it does so, it "tries" to induce a current in the coil which is in the opposite direction to the current causing the magnetic field in the first place. The result is that, for a short time, the current will increase towards its natural maximum value (determined by the supply voltage and the resistance of the wire) - but it will do so more and more slowly. In theory, it will never quite reach that maximum possible value, because the opposing current - though decreasing - is always present. In practical terms, however, the "main" current can be considered to reach that maximum value after a fairly short delay. This short-term event is called a transient.

When the electromagnet is switched off, another transient occurs - but a dramatically different one. The following diagram illustrates both transients:

That second transient is pretty spectacular, isn't it? What's going on?

When the current is switched on, energy is being fed into the electromagnet. For as long as the coil is switched on, that energy is manifested as the magnetic field.

When the current is switched off, that energy is still there - it doesn't just disappear. As the magnetic field collapses over a short time, a voltage appears across the windings, according to the principle of electromagnetic induction discovered by Faraday (see above). Because of the rapidity of the collapse - far quicker than the earlier build-up - this voltage is much greater than the battery voltage while the magnetic field was being maintained.

The process is akin to pushing a magnet into a solenoid rather slowly, and then waggling it backwards and forwards very quickly within the solenoid, with ever-decreasing strokes.

Why does the voltage after switch-off oscillate up and down?

It's all to do with Lenz's Law again. The voltage across the coil generates another magnetic field, in the opposite direction. This second field reaches a maximum, then collapses also - thus inducing another voltage across the coil, which then results in another magnetic field - and so on, with exponentially decreasing maximum values, until all the energy is dissipated. The result is a damped sinusoid. (Again, in theory, the process never finishes; but in reality, of course, it does, as losses occur all the time.)

A few reasonably simple comments about the frequency of the damped sinusoid:

The fact that the process is not instantaneous (even though it's pretty fast) is due to the coil's built-in stray capacitance. To a very small extent, adjacent turns in the coil behave like the plates of a capacitor, so that the coil may be thought of as an inductor in series with this "overall" capacitor. Such an arrangement has its own resonant frequency, which determines the rate at which the oscillations occur. The frequency is given by

f = 1 / (2 x pi x (square root of L x C))

where L is the inductance of the coil in henrys, named after Joseph Henry (1797-1878) , and C is the capacitance in farads. In simple terms, large inductances and capacitances lead to low frequencies, and small inductances and capacitances lead to high frequencies. (In an induction coil , high frequencies are desirable because they give rise to higher-voltage sparks from the secondary.)

The voltages generated - initially at least - may well be high enough to produce a series of sparks across the switch contacts. (They look like a single spark to a human observer, because they occur too rapidly for the eye to see them individually - but suitable photographic techniques may show what is really happening.) Really high-voltage sparks can be put to good use - notably, in a car ignition system - but this arcing across the contacts is a nuisance, partly because it causes damage due to oxidation. There are ways to deal with it. You can read more about the details of this in my later page about induction coils , which has links to some of my wacky little projects.

There's one more aspect of electromagnetic induction that needs to be mentioned before we finish.

As already mentioned, there are always some losses in transformers. These are due to a number of factors, including the resistance of the winding-wire itself; less-than-perfect "coupling" within and between the coils; - and eddy currents.

An electromagnet - i.e. a coil of wire wound onto a core of ferromagnetic material - can generate a more intense magnetic field than a solenoid can. The iron or similar material has the effect of concentrating the field more tightly.

However, the very presence of the core can cause problems. If it's made of a conducting material, and a varying power supply is used (for example, to run a transformer), the changing magnetic field in the windings will induce swirling currents in the core itself. As a result, energy that you'd normally want to be increasing the magnetic field strength (so as to generate a stronger output from a secondary coil, in a transformer) is going to waste - and, furthermore, having the undesirable effect of heating the whole thing up.

Eddy currents are not always a bad thing. If you want a heating effect, they're a very good thing. In electric furnaces and inductive hot-plates for cooking, the effect is deliberately promoted.

However, in most situations they're a nuisance. Various measures are often employed to eliminate or at least minimize the problem.

If you've ever looked at an ordinary transformer, you'll have noticed that the core is made up from thin pieces of sheet metal. Each of these is coated with some insulating material, and the whole bundle riveted or bolted together. Eddy currents will still occur in each individual slice; but overall, it's an effective way of keeping the losses down quite a lot.

You can see this in the following photograph of my little synchronous wheel . The former for the electromagnet was made from part of the core of an old transformer; the laminations (each about 1mm thick) are clearly visible.

In some special-purpose transformers and other applications, special non-conductive materials are used. For example, in the flyback (or line-output) transformer in a TV or computer monitor (a smallish but quite gutsy transformer which produces the high voltages needed to operate the picture-tube electron guns), the core is made from a ferrite - a salt of what would be ferrous acid , H2 Fe2 O4 , if it existed (it's unstable and can't be isolated). The material is an insulator, but it's also ferromagnetic - ideal for the job if you really don't want eddy currents. (There are other similar materials that can be used also.)

As you'll see in my induction coil pages , normally you do want to minimize eddy currents - but, in one of my projects of this type, they're not such a bad thing, in moderation. The core of one of my induction coils was deliberately made from a solid iron rod. Why? Well, you'll have to read the relevant page to find out!

A final comment on this, if I may:

I think it's sad that I wasn't born into an era when I could have been the discoverer of eddy currents. "Why's that?" I hear you cry. Well, because then I could have called them "Teddy currents", couldn't I?!

That'll do! Hopefully as a result of reading this, you've got some idea of what electromagnetism is all about. Don't worry if you don't understand it all. As I've hinted earlier in this page, I suspect that nobody really does! After nearly two hundred years, even though we know how to use the effects to make the quality of our lives better than ever before, there still seem to be lots of vexed issues.

But is that such a bad thing? Wouldn't it be a boring old universe if we all knew everything about everything, with no more questions to ask? If teachers knew all the answers, how would nerdy kids like me piss them off? Who wants that?

No thanks - that would be a "Nerd's Nightmare"!

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