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I. Electric field strength is expressed in units of newtons per coulomb (N/C).

Have you ever heard of something called force? I don’t know what a force is, but whatever it is, it makes things accelerate, that is it makes things speed up. You all know that if you apply a force to a baseball, the baseball accelerates until you stop applying the force. The British unit of force is the pound. The metric unit of force is the newton (N).

Have you ever heard of something called electric charge? You probably know that there are two kinds, positive and negative. The unit of electric charge is the coulomb (C). One coulomb of electric charge is ONE, BIG, HONKING quantity of charge. You probably have heard of the elementary particle, the electron. For our purposes, it is pretty safe to say that the electron carries the smallest possible electric charge, about one ten millionth of one trillionth of a coulomb of negative charge.

If you apply a force to an electric charge, it will accelerate. One way to apply a force to a charge is to push it by direct contact. Another way is to expose it to an electric field. You may have heard of the electric field. It is an example of a force field. Other examples of force fields are the magnetic field, and the gravitational field. Electric fields and magnetic fields are closely related.

An electric field somehow exerts a force on an electric charge, because when an electric charge feels the field, the charge accelerates. So, it would not be surprising if force were involved in a definition of electric field strength. If you get a larger quantity of charge, the same electric field will exert a greater force on the charge. So, we need more than just force to define electric field strength, since the force will vary depending on how much charge we have present. Double the charge, the force doubles. We can define electric field strength as force exerted by the field PER quantity of charge, that is force/charge. That ratio will stay constant no matter how much charge we put in the field to test the field strength.

It makes sense that the electric field strength ought to stay the same; regardless of how much charge we use to test it. Why would the field care what experiments we do? The field is the field. Same with gravity. The earth pulls harder on a big rock than on a small one, but the gravitational field strength doesn’t change just because you pick up a bigger rock.

So, if the electric field strength is defined as force/charge, then the units of electric field strength ought to be newtons/coulomb, or N/C. The units of electric field strength N/C can equivalently be expressed as volts/meter (v/m), but showing that, requires some additional development, and a little math.

Where does an electric field come from? One place is electric charge. An electric charge fills all of space with an electric field. All other charges in the universe feel a force due to that field. Where else can an electric field come from? An electric field is generated by a changing magnetic field. And that hints at the story of light, radio, and the whole electromagnetic spectrum. But we are not ready for that story yet. The truth of it would burn and blind you at this point.

II. An ampere (A) of electric current is defined to be one coulomb of charge flowing past a point every second; 1A = 1C/s.

You no doubt have heard of electric current I, and that it is measured in amperes, or amps (A). But what is an amp? It is defined to be one coulomb of electric charge flowing past some point in space, or some point in a wire, every second. That is, amps = coulombs/second. 1 amp = 1 coulomb/second or 1 A = 1 C/s. One coulomb is a lot of charge, and one amp is a lot of current. I’m ignoring the distinction between positive and negative charge flow, because I want to keep this simple, light reading. If we were doing calculations, we would definitely have to sweat the details.

You can put an electric field through a wire by putting the ends of the wire across a battery. I won’t tackle the details of how the battery does that. The electric field in the wire will start the electrons in the wire moving, and thus a current will flow. Some of the electrons in metals are free to move; and they do when they feel an electric field. Electrons in insulators such as plastic are not free to move, so putting a piece of plastic across a battery would not result in current flow.

When you buy a battery, you don’t ax for a battery that produces a certain electric field strength in a wire. You ax for a battery of a certain voltage, or number of volts. But what’s a volt?

III. The volt is the unit of electrical potential. Voltage tells you the amount of work that one coulomb of charge can do for you.

Before defining the volt, let’s define work. Have you ever done any work? Pick up a kilogram (weighing around two pounds), and lift it one meter. You have just done one joule (J) of work. In doing that work, you have stored energy in that kilogram mass you lifted. You can let it go; it will accelerate as it falls, and impart its energy of motion to your toe. Work and energy have the same units, joules. Work is just applying a force through a distance, such as lifting a book some distance off the table. When you do work, you often store energy. Stretch a rubber band. You have just done some work, and stored some energy. The stored energy in the rubber band can now do some work for you, such as accelerate a rock in a sling shot. Push an electron from the positive plate of a capacitor to the negative plate. It takes work to do that, because the electron wants to stay away from the negative plate, and go back to the positive plate (opposite charges attract). In moving the electron from the positive plate to the negative plate, you have done work, and thus stored energy. Now, you can let the electron go, and it will accelerate back to the positive plate. It can do work for you along the way, if you want to route it through a light bulb or electric motor.

Stored energy, or stored ability to do work, is called potential energy. The units stay the same, joules (J). If you let an electron “fall” from the negative side of a battery, through a wire, to the plus side, it can do work for you along the way. If two electrons fall, you get twice as much work. So, the amount of work that the battery can do for you depends on how much charge falls from the negative terminal to the positive terminal. The voltage V of a battery is the amount of work you get out if one coulomb of charge falls from the negative end to the positive end. Voltage is a measure of electrical potential energy. A one-volt battery will do one joule of work if you let one coulomb of charge flow from negative to positive. You could also say a one-volt battery will deliver one joule of energy if you let one coulomb of charge flow from negative to positive. Equivalently, a one-volt battery delivers one joule of work or energy, PER coulomb. Volts = joules/coulomb, or 1v = 1J/C. Electrical potential is frequently shortened to simply, potential. That’s dangerous, but ok as long as everybody concerned understands that electrical potential is what is really meant. It is very important to understand that the potential energy of a quantity of charge poised to fall from one end of a battery to the other is the total energy you are going to get out. The electrical potential energy is the energy you are going to get out if exactly one coulomb of charge falls from one end of the battery to the other. Potential energy is expressed in joules J. Electrical potential energy is expressed in joules per coulomb J/C, equal to volts v. The symbol for electrical potential is V, and its value is expressed in units of volts v.

IV. There is a simple relationship between the current through a wire, and the electrical potential between the ends of the wire: V = I x R.

I guess everybody knows Ohm’s Law. Ohm’s Law is an experimental result. Apply a voltage across the ends of a wire, and a current will flow. If you double the voltage, the current will double. If you triple the voltage, the current will triple. Whatever you do to the voltage, the same thing happens to the current. That means you can say that the current and the voltage are proportional. Ok, so you know that doubling the voltage, will double the current. Will that knowledge enable you to predict what current will flow if you apply, say, 1 volt to a particular piece of wire? No. All you know is that whatever current flows, it will double or triple if you double or triple the voltage. To predict the current flow for a certain voltage we need more than a mere proportionality, we need equality. We need an equation. Ohm’s Law is the equation, but how do we get it? Well, just start making measurements. Take a piece of wire, apply a known voltage to it, measure the current flow. Calculate V/I. Change the voltage, measure the current flow. Calculate V/I. Do it all again. And again. You will discover that all the V/I’s that you determined are the same number. That number is called the resistance R of the wire. Get a different wire. Go through the whole routine again, and you will discover that all the new V/I’s are all the same number, once again. That number is the resistance R of the new wire. So, for a given wire, V/I = R. And that’s Ohm’s Law. The resistance R is measured in ohms. The Ohm’s Law equation can be rearranged by simple algebra into two other forms: I = V/R, and the familiar V = I x R.

Ohm’s Law is valid for common metals, and several nonmetallic conductors. Ohm’s Law is valid only for constant temperature cases. If your wire is sucking so much current that it heats up, then your V/I ratios will not remain constant, meaning Ohm’s Law will fail. An example of a non-constant temperature case is a light bulb. As you turn up the voltage, the bulb draws more current, and the filament gets hotter and hotter (and brighter and brighter). Ohm’s Law would not hold true over a series of measurements on a light bulb drawing enough current to light up.

V. Magnetic field strength is expressed in units of N/(C x m/s), or teslas.

The magnetic field is probably more familiar to most people than the electric field, but it is harder to understand, and the units are more complex. If you hold an electric charge motionless in an electric field of constant strength, the charge will feel a force, and if you let go of it, it will start to accelerate. In contrast, if you hold an electric charge motionless in a magnetic field of constant strength, the charge will feel NO force, and if you let go of it, it will not move. The only way a magnetic field can exert a force on an electric charge is if the charge is moving, or if the magnetic field strength is changing with time. An electric generator works by exposing loops of wire to a changing magnetic field, and that changing magnetic field exerts a force on the electrons in the wire, making them move, thus generating a current. Recall that a few paragraphs above I said that a changing magnetic field produces an electric field. That’s what’s happening here. A changing magnetic field produces an electric field, and that electric field exerts a force on the electric charge.

Let’s say an electric charge IS moving in a magnetic field. The size of the force that the charge feels depends on the size of the charge (just like in the electric field case), but also on the speed that the charge is moving. Recall that in the electric field case, the field strength is expressed as force/charge, or newtons/coulomb or N/C. For the magnet field case, we have to include units of speed when we express the strength of the field, because the force exerted by the field on a charge depends on the speed of the charge. So, the units of magnetic field strength are force/(charge x speed), or newtons/(coulomb x speed), or N/(C x m/s). Why m/s? Because metric units for speed are meters per second, or meters/second, or m/s. Anyway, the whole mess, 1 N/(C x m/s), is defined as 1 tesla, or 1 T. The gauss is another unit of magnetic field you may have heard of. 10,000 gauss = 1 tesla.

Now, I’m trying to keep this as simple as possible so as not to drive people away. Becky Zed has already sed that this article needs punching up, and that she systematically avoids it. You physics types know that I have oversimplified here and there. Hell, from the point of view of Einstein’s Theory of Special Relativity, the magnetic field is just an illusion. There is only the electric field. One of the strange effects of making measurements on moving objects such as electrons flowing in a wire is the illusion that another field (magnetic) is present.

Having said that, what generates a magnetic field, at least classically (never mind Special Relativity) speaking? Magnetic charge? Nope. No such thing. A magnetic field is generated by an electric current. When electric charges move, a magnetic field is produced. How else? A magnetic field is also produced by a changing electric field.

Let’s recap a couple of important points. An electric field is produced by the presence of an electric charge, or by a changing magnetic field. A magnetic field is produced by an electric current, or by a changing electric field.

VI. Maxwell predicted electromagnetic waves, such as radio waves.

The greatest physicist of the nineteenth century, Scotsman James Clerk Maxwell, wrote down a set of partial differential equations that mathematically related electricity and magnetism. They are known as Maxwell’s Equations. They show that electricity and magnetism are different aspects of the same thing.

Two of these equations can be combined to produce a wave equation. A wave equation describes a traveling wave. Maxwell’s wave equation describes a wave composed of an electric field perpendicular (at right angles) to a magnetic field, the wave traveling in a direction perpendicular to the direction of the two fields. We call this an electromagnetic wave. Imagine changing magnetic and electric fields regenerating one another as they move through space -- that’s about the best you can do to describe with words how an electromagnetic wave can exist. Maxwell calculated the speed at which these electromagnetic waves should propagate. The speed he got was the same speed as the experimentally measured speed of light! Well, it became clear that light was an electromagnetic wave.

Other examples of electromagnetic waves are radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, gamma rays, and cosmic rays. All these electromagnetic waves travel at the speed of light. At the speed of light, you could travel around the Earth 7 ½ times in one second.

How do the above electromagnetic waves differ from one another? They differ in wavelength. The wavelength of any train of waves is just the distance between the wave crests.

The wavelength times the frequency of a train of electromagnetic waves equals the speed of light, c. Wavelength x frequency = c. Frequency is just the number of wave crests passing your antenna each second. A frequency of 3765 kHz, or 3.765 MHz means that 3,765,000 wave crests pass your antenna each second.

VII. Radiation components from a half-wave antenna.

This topic is not basic electricity, but I think it’s interesting and I want to write about it. I don’t want to make it a separate link on the blog page, so I’ll just stick it here in the basic electricity article. Better here than in Becky Zed’s chocolate peanut butter cake recipe, eh?

The radial dependence of dipole fields has three distinct regions: the static, induction, and radiation regions. I am only interested here in the static and radiation regions. The static region is defined as the region much closer to the antenna than a distance of one wavelength. The radiation region is defined as the region much farther from the antenna than a distance of one wavelength. Let’s look at the radiation region first; that’s the region usually of interest to hams.

In the radiation region the electric field is dominated by a 1/r radial dependence, where r is the distance to the antenna from a point at which you might be making a measurement. This can be deduced from an analysis of the expression for the electric field strength of a half wave dipole antenna. The equation is gruesome, and there is no need to present it here. A 1/r radial dependence simply means that within the radiation region, if you double your distance to the antenna, then the electric field strength will decrease by a factor of 1/2, that is, the electric field will be reduced to only 1/2 of what it was. If you triple your distance to the antenna, the electric field will be reduced to only 1/3 of what it was. The power in the field varies as E², that is, the electric field strength squared. So if the electric field in the radiation region has a1/r dependence, then the power dependence is (1/r) ², or 1/r². This is the inverse square law dependence familiar to hams. If you double your distance to the antenna, then the power in the field will decrease by a factor of 1/2², that is, the power will be reduced to only 1/(2x2) or 1/4 of what it was. If you triple your distance to the antenna, then the power will be reduced to only 1/(3x3) or 1/9 of what it was.

In the static region the electric field is dominated by a 1/r³ radial dependence. That means that within the static region, if you double your distance to the antenna, then the electric field strength will decrease by a factor of 1/2³, that is, the electric field will be reduced to only 1/(2x2x2) or 1/8 of what it was. If you triple your distance to the antenna, then the electric field will be reduced to only 1/(3x3x3) or 1/27 of what it was. Once again, the power in the field varies as E². So if the electric field in the static region has a 1/r³ dependence, then the power dependence is (1/(r³)) ², or 1/(r³) ², or 1/r⁶; a much stronger radial dependence than the 1/r² dependence that you are familiar with for the radiation region. If you double your distance to the antenna in the static region, the power in the field will decrease by a factor of 1/2⁶, that is, the power will be reduced to only 1/(2x2x2x2x2x2) or 1/64 of what it was! Compare that to the 1/r² dependence in the radiation region, where if you double your distance to the antenna, then the power drops to 1/(2x2) or 1/4 of what it was. 1/64 vs.1/4.

The static field with its 1/r³ dependence is suitable for high-security communication because of its short-range nature as compared with the 1/r radiation field. As an example, let us take the desired working signal of the electric field to be 1 micro volt/cm = 1 x 10^-6 V/cm, and the minimum detectable signal to be 1 x 10^-2 micro volt/cm. So the minimum detectable signal is 1/100 of our working signal, that is, E_near/E_far = 1/100. If the communication is desired to cover a distance of r_near = 2 km, then the distance r_far at which the field becomes undetectable is obtained by solving the equation E_near/E_far = 1/100 = (r_near / r_far ) ³ = (2km / r_far ) ³ for r_far. Thus r_far = (800) ^1/3 = 9.8 km. The field becomes undetectable at 9.8 km. If you do this same calculation for the radiation field, the field does not become undetectable for a full 200 km! The bad guys far away can hear your secret shit.

So what is the bottom line here? Pick a frequency of operation that has a corresponding wavelength that is much, much longer than the distance over which you want to operate. If you do that, and use minimum necessary power output, then the field will drop to undetectable levels just a few times farther out than your working distance. If you do not do that, and you use a wavelength much shorter than your communications distance, then you will be using the radiation field, and the field will not drop to undetectable levels for a distance of 100 times your communications distance! The bad guys may hear you.

In the example above, we need a frequency with a corresponding wavelength of much greater than 2 km, say 100 km. The frequency with a corresponding wavelength of 100 km would be 3 kHz, a very low frequency. But VLF maritime communications is nothing new. Such long wavelengths also have the advantage of bending around the curve of the earth more readily than short wavelengths, making possible very long distance surface wave communication.

I remember back around 1982, I toured Carlsbad Caverns. It was a self-tour, on which I carried a little radio receiver that picked up low power broadcasts from radio transmitters located near various rock formations. I listened to narration about the formations, on the receiver. I remember thinking how remarkably fast the signals dropped to zero as I walked away from any particular formation that had narration. Over just a few feet the signal dropped to zero. I bet the broadcast wavelength was much longer than a few feet, meaning that they were using the static field, which, as we have seen, drops off VERY fast.