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By I Catt, Walton and
Davidson. Wireless World, March
1979. |
The History of Displacement Current |
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[Figures missing.] Previous article
; Second version Scandals in
Electromagnetic Theory http://www.ivorcatt.com/28scan.htm In the early nineteenth century electromagnetic
theory made advances, a cornerstone of the theory being the doctrine of
conservation of charge q, which developed into the doctrine of continuity of
electric current flow, dq/dt = i. In the middle of that century Maxwell
struggled with the paradox of the capacitor, where charge entered one plate
and then flowed out of the other plate apparently without traversing the
space between the plates (Fig.1 missing) [see Figure 64 ]. It seemed that electric
charge was being destroyed on the upper place and being re-created when it
reappeared on the lower plate. Maxwell "cut the Gordian knot" as
Heaviside put it (Electromagnetic Theory 1893 p28 sect.30; p441 sect.218) by
postulating a new type of current, called "displacement current",
as flowing across the gap BC in Fig.1 [see Figure 64 ] so as to save the
principle of continuity of electric current. "Displacement current" was a
result of his postulation of "electric displacement". Maxwell said
that the total outward displacement across any closed surface is equal to the
total charge inside the closed surface. (Maxwell 1873). [Comment by Ivor
Catt, sep03. Here my article seems rather muddling. The reference does give
the postulation of "Electric Displacement", so creating the new
idea of "the total movement of electricity" which causes magnetic
field, resolving the problem of the capacitor, but here it is mixed up with
Gauss's Law.] It is not surprising that objections were
raised. Notice, in Fig. 2 [wire AB, then a gap, then wire CD], that if in any
circuit there should be a break, BC, in the current path, we are bound by the
principle of conservation of charge to say that the current i, that is the
flow of charge, entering B from A accumulates as charge Integral idt at B,
and the current reappearing at C "accumulates" equal negative
charge minus integral idt. By definition, electric displacement outward from
B equals the total charge trapped at B; D = integral idt, and i = dD/dt. It
is not a coincidence that "displacement current" saves the idea of
continuity of electric current; it does so by definition. With the
postulation of displacement current, it would never in future be possible to
devise an experiment which might refute the principle of continuity of
electric current. Popper would therefore say that "displacement
current" is an unscientific concept (Popper 1963). Whenever charge seems
to disappear at a point, displacement takes its place. Whenever electric
current seems to disappear at a point, displacement current takes its place. It is important that Maxwell and Heaviside
believed that the current entering a capacitor plate became trapped and had
nowhere to go. Writers on the subject must be glad that some route between B
and C for real current did not declare itself, since they say that the
brilliant postulation of displacement current led to the postulation by
Maxwell of waves in space. Meanwhile, even as Maxwell was contemplating
the ethereal displacement current, practical electricians were inventing and
building wired telegraph systems. The distortion of signals travelling long
distances was bad, and was thought to be due to the fact that the capacitance
of the telegraph wires had to be charged up through the resistance of the
wires, resulting in an RC time constant which attenuated different
frequencies differently. As late as 1910 virtually all electricians
(including Lord Kelvin) did not accept Oliver Heaviside's claim that a
telegraph wire had distributed inductance as well as capacitance, and that if
only this inductance were increased by the addition of periodic loading
coils, distortion-free transmission over long distances could be achieved
(Heaviside 1893). It was important for Heaviside to encourage
a sensible approach to the characteristic impedance of telegraph lines,
because the practical pay-off in telegraphy and telephony would be immense.
(This misunderstanding delayed the introduction of telephones for twenty
years.) This practical pay-off would be best achieved by arguing that signals
travelling down (between) telegraph lines were undistorted TEM and similar to
the waves in space discovered by Hertz in 1887, twenty years before, and
previously postulated by Maxwell as one implication of his proposed
displacement current. It was important for Heaviside not to
criticise the theory he was trying to argue from, Maxwell's electromagnetic
theory. So it would have been injudicious for Heaviside to question the
concept of displacement current, and he never did. The essence of the concept of a transverse
electromagnetic wave, TEM, is that nothing - field, flux or current - flows
laterally across the surface of the wave front. The analogy is the Severn
Bore, where we see a single step of water rushing up the River Severn.
Everything ahead of the step is steady, and everything behind the step is
steady. There is no lateral, sideways flow. In the electromagnetic case (Fig.
3) [See Figure 5 . Also see animation ] ,
the idea of a lateral flow of current across the face of a TEM wave is
absurd, and would result in a longitudinal magnetic field; the step would
"get ahead of itself". Further, since the step travels forward at
the speed of light 1/ \/me , any lateral flow would cause embarrassment by
travelling even faster, in the same way that when you walk across inside a
moving train by Pythagoras' Theorem you are travelling faster than the train. Now although in the case of a capacitor,
displacement current needed to be regarded as just like a real current, for
instance causing a magnetic field; in the case of the D flux at the front of
a step of TEM (ExH) energy current travelling down a telegraph line, the
displacement clearly must not behave like a real current - for instance by
creating a magnetic field which would reach out ahead of the wave front and
ruin its TEM nature. Maxwell and later Heaviside did not notice
the discrepancy in the requirements of displacement current; that in a
capacitor it must act like real current but in a transmission line it must
not; because neither of them knew that a capacitor was no more nor less than
a transmission line (Wireless World dec78, p51). This is even today known by
very few scientists. Maxwell, along with today's text book writers (e.g. Fewkes 1956 ; Bleaney 1957 , [ Fishbane 1993 ; Resnick 2001 ;] ), believed that
the displacement current dD/dt travelling across between the plates of a
capacitor BC was uniformly distributed, and it is only very recently that it
has been pointed out that the flow of current and field in a capacitor is
identical with that in a transmission line; that the field moves out from the
capacitor's leads as if they were links to one end of a transmission line. So
the discrepancy could not become apparent. A serious difficulty for displacement
current arises when we realize that the two plates, BB', CC' in Fig. 4, are
a transmission line. We know that the current I travelling down to B from A
then flows out sideways from B along the capacitor plate BB'. This route,
along the capacitor plates, failed to declare itself to Maxwell, and everyone
has followed his lead. In the transmission line (Fig. 4) [ Figure 5 . Also see animation
] , everyone agrees that the current
i entering the line at B leaves B by flowing along the line BB'. No displacement
current dD/dt between the lines is needed for us to retain the doctrine of
conservation of charge and conservation of current. In fact, if this dD/dt were
regarded as a current, far from saving the doctrine, it would destroy it,
because now more current ( i + dD/dt ) would be leaving the first section of
the line BB' than was entering it. The last sentence is difficult to grasp;
no matter, because it is easy to see, and sufficient to see, that if i enters
B from A and i leaves B along BB', continuity of current is preserved without
our having to postulate displacement current. "But surely we cannot just drop
displacement current when for a century every expert (e.g. Solymar 1976,
Winch 1963) has been protesting that it is the foundation of our craft; that
'Maxwell's leap of genius' in proposing displacement current was what got the
subject going - leading to Hertz's discovery of waves in space, for
instance?" The answer lies hidden in Heaviside's
magnificent, regal statement, "We reverse this." In his Electrical
Papers, vol. 1, 1892, page 438, Heaviside wrote; Now, in
Maxwell's theory there is the potential energy of the displacement produced
in the dielectric parts by the electric force, and there is the kinetic or
magnetic energy of the magnetic force in all parts of the field, including
the conducting parts. They are supposed to be set up by the current in the
wire. We reverse this; the current in the wire is set up by the energy
transmitted through the medium around it…. The discrediting of displacement current
merely makes Heaviside's "We reverse this" mandatory. It means that
the field must be the cause and electric current an effect, rather than (as
Maxwell thought) the other way round. If we keep to "Theory H", the
theory that the field ExH, travelling along between the wires at the speed of
light - what Heaviside called the "energy current", is the cause,
then electric charge and electric current are merely what define the edge
of an energy current. If electric current is that which defines the side of
an energy current, then we may with equal justification postulate
"displacement current" as that which defines the front face of a
step of energy current. Under "Theory H", Maxwell's 'leap of
genius' (in postulating displacement current and thence waves in space)
becomes tautological; "Because a wave in space if it existed would have
to have a front face (displacement current), then I propose such a front face
and therefore I propose waves in space." Maxwell would have saved us a century of
confusion if he had had enough insight to say; "Since circuits
containing capacitors, that is, open circuits, work, it follows that the
essence of electromagnetics cannot be electric current in closed circuits of
conductors; it must be something else. What about waves in space?"
Heaviside, seventy years later, missed the key point by a whisker. He failed,
but he failed gloriously. He never discovered the flaw in the structure,
displacement current. References Bleaney, B. I. and Bleaney 1965,
Electricity and Magnetism, 2nd Edn (Oxford: Clarendon) p. 258 Fewkes, J. H. and Yarwood 1956, Electricity
and Magnetism, Vol. 1 (London: University Tutorial Press) p. 505 Heaviside, O., 1893, Electromagnetic
Theory, (London. Reprinted New York: Chelsea Publishing 1971) p. 28 section
30; p. 441 section 218. Maxwell, C. J., 1873, A Treatise on
Electricity and Magnetism, (Oxford: Clarendon) [vol. 2] p. 253 Popper, K. R., 1963, Conjectures and
Refutations, (London: RKP) p. 37 Solymar, L., 1976, Lectures on
Electromagnetic Theory, (Oxford: OUP) p. 6 Winch, R. P., 1963, Electricity and
Magnetism, (Englewood Cliffs: Prentice-Hall) p. 387 Typed by Ivor Catt 12feb99/sep03. Figures
missing. This article is by Catt, Walton and Davidson, as was the previous
one, "Displacement Current",
Wireless World, dec78. Comments
a quarter of a century later by Ivor Catt The intrusion of Popper in the March 1979
article above is unfortunate because too sophisticated. The key argument is
the crucial realisation by Catt in the 1960s and 1970s that remained
unnoticed* until that moment. Catt realised
that since a capacitor has physical size, so charge entering a capacitor then
has to spread itself out across the capacitor plate. This takes time, and
introduces a further stage in the process when a circuit contains a
capacitor. This stage was ignored (because unnoticed) by Maxwell and
Heaviside and those who followed. When we insert that stage, the whole story
leading up to Maxwell's postulation of Displacement Current and beyond
collapses. Ivor Catt 19sep03 * At the same time as it was remained unnoticed, it is possible that
engineers at UKAEA Culham, and other "big bang", "plasma"
honchos knew that when they discharged a large bank of large capacitors into
their toroid to create hot plasma, the charge exiting from each capacitor
came out as if from a charged transmission line. [Certainly, decades later, I
seem to remember that one such made this claim to me.] However, such
practical men did not think about Maxwell's Equations and the origin of
Displacement Current, which they came across, if at all, some years before in
University when they were taught that they were second rate, second class
graduates, and so should go into industry, never to talk lecture to awed
students about Maxwell's "leap of genius". Those (previously first
class graduates) who said such things to awed students never had cause to
discharge a large bank of capacitors at one instant. Their capacitors were as
depicted in their text books and course notes, with the wires entering the
plates at the centre, not at one end. Entry at the centre of the capacitor
plate successfully camouflaged the reality, that a capacitor was a
transmission line. Ivor Catt,
19sep03 My 1994 book "Electromagnetism 1"
is at http://www.ivorcatt.com/em.htm |
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Theory of Flight. http://www.ivorcatt.com/2606.htm
Displacement Current http://www.electromagnetism.demon.co.uk/z001.htm
http://www.ivorcatt.com/2635.htm
Catt Question http://www.ivorcatt.com/28anom.htm http://www.electromagnetism.demon.co.uk/catanoi.htm
Maxwell's Equations
http://www.ivorcatt.org/ic3804.htm http://www.ivorcatt.com/2804.htm
Moving Backwards. http://www.ivorcatt.com/2607.htm
TEM Wave. http://www.electromagnetism.demon.co.uk/17136.htm
http://www.electromagnetism.demon.co.uk/20136.htm
The Heaviside Signal http://www.ivorcatt.com/2604.htm http://www.ivorcatt.com/1_1.htm figures 4, 5. |
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