Reading Steinmetz, part 2

September 5, 2012 11:22:57 PM CDT

Last time I cut off at the end of the preface, which was admittedly a weak start. I did so because I was already a few hundred words in, and Steinmetz starts Section 1 with the information density set to 'high'.

Section 1:

His general approach to explaining electricity shows evidence of a practical background: he tells you how to generate it.

First he defines the unit magnet pole as the reference value for magnetism. If you put two unit magnet poles 1cm apart, they generate enough force to accelerate one gram at one centimeter per second squared.. a unit called the dyne, the centimeter-gram-second system's equivalent to the meter-kilogram-second system's Newton. One dyne is 10 millionths of a Newton.

That amount of magnetic field strength is represented by one magnetic line per square centimeter, or 4π lines across the surface of a unit sphere (a sphere with radius 1) with the unit magnet pole at its center. Remember that.. it will be important later.

Next he tells how electric currents can generate magnetic fields.. no deep physical explanation of it, he just says that it just does.. the main point being that a magnetic field fills the space around a conductor with current passing through it. The interesting bit is that the lines of magnetic force form circles around the conductor. If we assume the conductor is a straight wire, you can imagine the magnetic field as a rotating tube surrounding the wire.

To understand the rotation, imagine a dot on a rotating circle. No matter where the dot starts, the rotation will eventually take it back to its starting point.

That 'ending up back where you started' business is the defining characteristic of what physicists call a 'circuit', so Steinmetz says the magnetic field forms a magnetic circuit around, and perpendicular to, the electric circuit.

That shouldn't be any surprise if you've gone through college or advanced high school physics, but it was fairly big news back in the day.

The idea that probably wasn't mentioned back in physics class was the length of a magnetic circuit. That's what allows us to define electrical current in terms of a magnetic field. The unit current is one that produces a magnetic field that's just as strong as a unit magnet pole: 1 magnetic line per square centimeter, or 4π magnetic lines in a magnetic circuit of length 1.

Magnetic circuits form circles, and the distance around a circle is 2π times the radius. To get a magnetic circuit of length 1, you need a radius of 1/2π, or about . 15915 centimeters.

That sucks for anyone who likes to define things in numbers that are easy to remember, but fortunately, the 4π field intensity also sucks. If we combine them, we get 4π divided by 2π and all the parts that suck cancel, leaving 2. So: the unit current generates a field strength of 1 magnetic line per centimeter at a distance of 2cm from the wire.

The Ampere is one tenth of the unit current.

Next comes another important concept in electromagnetic theory: the turn.

So far we've been talking about electrical circuits where the current flows down a straight wire. If the wire loops back to where it started (or reasonably close to it), we have a 'turn'.

The thing about turns is, the magnetic circuits around them stack up. The magnetic field around two closely-spaced turns will be just as strong as the field around one turn with twice as much current running through it. That freedom to trade current for turns will come in handy when it comes time to design generators.

Current flowing through a turn creates a magnetic field, and the energy which does it is called magnetomotive force (MMF), and is measured in ampere-turns. If you normalize MMF by dividing by turns per centimeter (or inch, or cubit, or whatever), you get a value called magnetizing force.

Having gotten this far, Steinmetz goes off on what I consider a tangent dealing with superposition of parallel or opposing magnetic fields. It's useful information (the magnetic circuits around parallel wires with opposing currents push away from each other, the magnetic circuit moving down the center of an arbitrarily long helix is a straight line), but it's more geometry than electricity or magnetism.

He then comes back and repeats the definitions of some useful values:

  • Magnetomotive force is the energy of the whole circuit, and is measured in ampere-turns.
  • Magnetizing force is the amount of energy per unit distance, and is measured in ampere-turns per centimeter.
  • Field intensity is measured in magnetic lines per square centimeter.

Now, field intensity is a slightly misleading concept, because some materials are more magnetic than others. The same magnetizing force will produce more magnetic lines per square centimeter in a highly magnetic material than it will in a nonmagnetic material.

To sort out the ambiguity, Steinmetz makes our definition of field intensity more specific by saying that it only applies to air (or, more technically, a vacuum, the measured difference being approximately bupkis). He then introduces the term permeability to mean the ratio between 'the number of magnetic lines a given magnetizing force will produce in some non-air material' and 'the number of lines that same force will produce in air'.

To wrap up the final loose end in the package, he calls the number of lines produced in a non-air material the material's magnetic induction.. the number of magnetic lines induced in the material by a magnetizing force. The term field intensity is hereby limited to discussions about the number of magnetic lines in air.

This being a textbook, he then closes with a set of exercises, some of which are suspiciously specific:

  • What's the total magnetic flux per kilometer between the wires of a transmission line if the conductors are #0 Browne and Sharpe wire and the distance between them is 45cm?
  • How many ampere-turns are necessary in an alternator if each pole has to carry 6. 4 million lines of magnetic flux, given a laundry list of dimensions and permeabilities?

Fortunately, he works through the math so you can follow along, rather than making you wear out a box of pencils in frustrated speculation.

Wrapping up

And that's it for Section 1. Next up, Section 2.. some good stuff there, notably a "heres's how you do it" definition for electromotive force (aka: voltage).

Random brain cookies:

I have yet to see any problem, however complicated, which, when looked at in the right way, did not become still more complicated. -- Poul Anderson