Not having a full collection of magazines is a real disadvantage
when multiple part stories are published and some editions are missing.
Such is the case here with Milton Kiver's series on electronics
design. I do have other parts of the series, but they have not been
posted on RF Cafe yet. However, each installment is pretty
much independent of the others. This month's topic is on the fundamental
theory of electrical potential and force. The name 'Maxwell' is
mentioned, but not in the way that strikes fear in the heart of
engineering students being introduced to the integral and differential
forms of his
eponymous equations (I know first-hand),
so it's safe to keep reading. First semester physics books cover
the same material, but since you night not have one handy, here
Theory and Application of U.H.F.
By Milton S. Kiver
Part 10. An explanation of the importance of the electric field
theory of Maxwell's equations in describing u.h.f. phenomena. A
subsequent article will cover a similar explanation based upon the
Fig. 1. - Showing the relationship of force vs. distance
between electrical charges.
The name of Maxwell seems to be ever present in describing ultra-high-frequency
phenomena and this perhaps, is as it should be, since without his
work it might have taken a great deal longer to fill out the ideas
on wave propagation.
The set of equations that form the basis for the electromagnetic
theory are called Maxwell's equations, although he is not solely
responsible for most of them. All these equations are expressed
either in ordinary differential form or compactly placed by means
of vector analysis. Neither will be used here since it is the avowed
purpose of these article to use very little mathematics, so (with
apologies to Maxwell) an attempt will be made to discuss these important
relations without the benefit of the exact science. With this explanation
as a background it should be much easier to comprehend some of the
properties of wave guides, cavity resonators, antennas, and any
other device that depends for its action on the above-mentioned
Maxwell's equations are generalized statements on the behavior
of electric and magnetic fields. The electric laws are based on
the observed behavior of the electron and the influence it exerts
on other nearby electrons. It would have been just as easy to have
based all our findings on the proton (positive charge) behavior,
but since the electron is the more mobile of the two it is easier
to deal with its properties. For the magnetic laws it is necessary
to go back to the properties of a magnet and see its actions and
reactions when brought near other substances that are affected by
it. When all these important facts are tabulated, there are four
(sometimes given as five) statements that form the starting point.
These four (or five) equations are known as Maxwell's equations.
Now to see just what these equations mean. They set down a set
of rules by which the science of electromagnetics has been developed.
As long as these rules are followed, all is fair; but if any deviations
are introduced, then the fundamental principles of the science are
being ignored and something else is now being engaged in; another
game - so to speak. There is nothing wrong in modifying the rules
if it is found that experience dictates such a change. But so far
Maxwell's equations have predicted all the observed results so it
is safe to assume that they are entirely correct and no attempt
should be made to change any of their forms.
These equations may be looked upon as four walls to keep the
players within certain confines. While in these boundaries they
may make other limitations, such as having the electric or magnetic
fields restricted to one direction, but this is still within the
game since the general rules are in no way being altered. The rules
are just not being used to their fullest extent - that is all. Since
the equations work in one, two, or three dimensions, it is possible
to use the above restrictions and still arrive at correct results.
Fundamental Electrical Theory
Fig. 2. - Indicating the distribution of force about
an electric charge by means of equipotential lines.
Fig. 3. - The use of lines of force and equipotential
lines in radio tubes.
Before any discussion of the above equations will be undertaken,
it would be advisable to review the foundations of all electric
and magnetic theory. The electric field will be dealt with first.
Any electric charge, such as an electron, exerts a force upon other
charges near itself. This force, while being just as much a force
as the gravitational pull or the force exerted by a machine, does
not apply to every material body in the universe but only to other
electric charges. If these other charges are positive, the force
is one of attraction while if they are negative, it is a repelling
force. Now, for many people the idea of just showing a charge without
indicating its force was rather hard to understand, so whenever
an electric charge is shown, lines radiating away from this charge
are also drawn and these lines are called lines of force. They are
the pictorial representations of what cannot be seen but what is
quite definitely there, namely, the force itself. Fig. 5 shows these
various lines, both for attraction and repulsion.
In addition to the representation of the electric lines of force,
as in the above figure, it is also possible to indicate the distribution
of electric forces as in Fig. 2. Here instead of lines of force,
we have all the points that have the same force exerted on them,
connected by one line. Because of the symmetry of the field about
the electric charge, these equipotential lines happen to be concentric
circles. However, this is a special case and will not always occur.
The circles closest to the center have the greatest force exerted
on them, while the farther away we get from the central electric
charge, the less the force.
Note that the equipotential lines never cross each other. If
one were to place an electric charge on an equipotential surface
or line then it would require no work at all to move this charge
along this equipotential line because the charge is neither being
moved toward or away from the central electrical charge. Radio engineers,
especially those engaged in tube manufacture, use charts illustrating
the equipotential lines and fields of force within tubes quite extensively.
To illustrate, refer to the diagrams of Fig. 3.
In Fig. 3A, we see that in a simple diode having a cylindrical
plate, the lines of force are radial from the plate to the cathode.
The equipotential lines are also drawn and an electron leaving the
cathode will try to reach the plate by the shortest route. The shortest
route will be along the path where the force that is exerted by
the plate is greatest. This will always occur along the lines of
force or at right angles to the equipotential lines. Hence, the
electron will travel in a straight line from cathode to plate.
In Fig. 3B we have the deflecting plates of a cathode-ray or
television tube. The electron beam, in speeding toward the fluorescent
screen, must pass between these plates and while in this region,
Will be subjected to the electric field that exists there. The plate
that is more positive will attract the negative electron beam and
cause the beam to deflect in this direction. The stronger the voltage,
the greater the deflection.
Here we have merely two examples of the use of visualizing electric
forces and electric fields and how they are utilized, whether directly
or indirectly, in radio apparatus.
The regions that the electric forces act in are called electric
fields and, in the literature of the subject, are quite often referred
to. These electric fields can be explored by taking other electric
charges and placing them under the influence of these fields of
force. From the way these outside charges act it is possible to
tell the direction of the force in these fields and just how intense
the field strength is. By experimenting with electric fields of
various strengths and noting different reactions on charges placed
in these regions, it is possible to arrive at rules which govern
the behavior of all such situations. Thus the first step, experimentation,
will lead on to the next point where it is possible to express all
the facts in a law or formula and which will cover all data taken
under similar conditions. For the case just mentioned there is Coulomb's
Law which states that the force acting between two electric charges
(or what is the same thing, two electric fields, since fields are
produced by charges) is directly proportional to their strengths
and inversely proportional to the square of the distance between
them. Using the formula notation, it is
q1 is the amount of charge of one unit
q2 is the amount of charge of the other unit
d is the distance between them
F is the force brought on by placing the two charges close to
Before going much further it might be advisable to point out
that while the terms electric field and electric intensity are sometimes
used interchangeably, they are really separate. The electric field
refers to the region or place where the electric intensity or electric
force acts and is not actually attached or connected to this force
in any way. It is quite analogous to a pitcher or container of water
and the water itself. Both are distinct and yet when placed on the
dinner table the two terms are used interchangeably. In the same
sense, electric field electric field intensity and just plain electric
intensity may be considered one and the same as far as it will be
Laws for Electric Fields
Fig. 4. - The number of lines of force leaving any electrical
charge is (by definition) equal to 4π
x the charge.
Fig. 5. - Configuration of electric lines of force, (A)
for attraction and (B) repulsion.
The next phase that interested the scientists after they had
formulated the ideas of electric charge and electric force or intensity
was to get the exact relationship between the charge and the amount
of electric field intensity due to this charge. The problem was
this: Suppose there was some charge inside a hollow sphere. How
is the number of lines of force or how is the electric intensity
related to this charge Q?The answer is known as Gauss' Law and in
words it states that the net outward electric flux (or lines of
force) from any charge in all directions is 4π times the
amount of charge Q. See Fig. 4. Thus there are two fundamental relationships
that hold in a region containing electric charge:
1. First is Coulomb's Law and this sets up the idea of electric
charges and the forces between them.
2. And second is Gauss' Law which gives the exact relationship
between the force set up by any charge and the amount of the charge
It is to be noted that whenever lines of force are drawn they
are always shown with arrows (Figs. 2 and 5). These arrows are meant
to indicate the direction in which the electric force due to the
charge act. The electric theory was first developed by men who postulated
that the lines of force should have arrows on them pointing in the
direction that a positive charge, if placed near any electric charge,
whether positive or negative, would go. This means that if a certain
space were filled with protons or positive charges, then all the
lines of force would point away from these positive charges since
they would repel an exploring positive particle in this field. On
the other hand, negative charges would attract this exploring positive
charge and so the arrows on the lines of force connected with negative
charges point toward the charge itself. All this sometimes tends
to be confusing and so it is better to just think of these lines
of force as an actual force which will attract oppositely charged
particles and repel like charges.
With this in mind, no confusion should result. These lines of
force are continuous, starting out from positive charges and ending
up on negative charges. Should the space in question contain only
positive charges, then the lines of force due to these charged particles
will continue indefinitely out into space toward infinity, and a
force would everywhere be felt. This is theoretically true but in
an actual case the effect of its electric intensity would be confined
to the immediate vicinity since from Coulomb's Law it can be seen
that force varies inversely as the square of the distance. At a
distance of say 8 centimeters from a charge the force would be 1/16
of what it is at 2 centimeters from the same charge, so it is obvious
that no great distance is needed before the overall effect of the
electric field is negligible. A clear idea of the way these forces
decrease with distance can be obtained from Fig. 1.
Turning now from the static case, let us put an electric charge
(for example, an electron) into motion and see if any new facts
are discovered. The easiest method of accomplishing this end is
to use a conductor, that is, a substance that contains a large number
of free electrons. Since the free electrons will experience a force
when any electric field is brought to bear on them, they will be
forced to move and the number that will flow past any point in this
conductor will be determined by the strength of the electric force
that is causing them to move plus the ease with which they can travel
through this conductor. Does the last statement sound familiar?
It should, for although it is never stated this way, it the good
old formula E = IR which is Ohm's Law. Note that a steady electric
field or electric force is used here - a situation that is true
for direct-current circuits.
Since the electron has a charge it will produce an electric field.
But it has been found on investigation that when put into motion
the electron will likewise give rise to a magnetic field. In 1819
the Danish physicist Oersted discovered that current in a wire affected
a compass that was held near this wire. Since compass needles will
only move under the influence of magnetic fields, Oersted concluded
that there must be a magnetic field about a wire carrying a current.
A little while later Ampere carried this one step further and
showed that two wires with currents in them exerted forces on each
other. With the two wires separate and distinct from each other
it must have been the magnetic field that reacted. It is from the
above that the first ideas on the relationship between electric
and magnetic fields were brought into existence and slowly started
the trend that ended with Maxwell's formulation of the electromagnetic
The type of magnetic field produced depends on the type of electric
current that is flowing in the wire. A steady flow of electrons
will produce a magnetic field that is likewise constant in value,
while changing magnetic fields are the product of changing electric
This idea of electric currents giving rise to magnetic fields
was proved time and again and was accepted without question in the
19th century. However, in the theories that Faraday and, a little
later, Maxwell envisioned about electrodynamics, there was more
to the story than just the above. Must currents always be present
for magnetic fields to occur? - questioned Maxwell. Was it not possible
to deal only with a varying or changing electric field and derive
magnetic effects from this? Maxwell claimed that it was possible
and so added this revision to the existing electric field equations
that were accepted at that time. He postulated two types of currents;
one was called conduction current and this was our ordinary flow
of electrons along any good conductor. The second type of current,
due not to actual moving electrons but rather changing electric
fields, he called displacement currents. Both, he said, gave rise
to magnetic fields.
A classical example to illustrate the above is given with a fixed
condenser in a setup such as shown in Fig. 6. Closing the battery
switch will cause current to start flowing in the circuit. Since
electrons do not flow across the space between the plates, it might
be said that the circuit is open at this point. However, since the
number of electric lines of force between the plates are changing,
due to the charging effect of the condenser, then, according to
Maxwell, the circuit is now no longer open at this point. Instead
of electrons or conduction currents flowing across this space, we
now have a displacement current and the circuit is continuous. It
would even be possible to detect a magnetic field produced between
the condenser plates during that portion of the time when the condenser
is charging up and the electric field is varying in this region.
The entire process ceases, of course, when the condenser becomes
The above was all that was needed to allow Maxwell to set up
his basic equations. From these he developed the idea that electromagnetic
waves travel through space at. a finite or measurable velocity which
we know to be approximately 186,000 miles per second.
Electric and Magnetic Fields
If the reader is a bit puzzled as to why Maxwell needed this
added idea of changing electric fields giving rise to magnetic fields,
let him pause for a minute and stop to consider that in the space
between the transmitting antenna and the receiving antenna there
is no flow of electrons at all.
Posted November 10, 2014