“Because the electric field is uniformly spread over the plates ….”.
“Fundamentals of Physics” by R Resnick and J Walker, pub. Wiley 2001, p761
“32.10 Displacement Current
“…. Assuming that the electric field E between the two [capacitor] plates is uniform …. …. Because the electric field is uniformly spread over the plates, the same is true of this fictitious displacement current ….”
“Electromagnetism Second Edition” by S Grant and W R Phillips, pub. Wiley 1975/1990, p353
S Grant and W R Phillips, Department of Physics, University of Manchester
“Displacement current was introduced by Maxwell in 1862. With the benefit of hindsight it seems surprising perhaps that people should have thought Ampere’s original law would apply to non-steady currents. However the original law correctly described the results of all the experiments made with the slowly changing currents which were met in the laboratory at the time of Maxwell. ‘The form of the rules we write down is more general than the experience from which they are culled, and it is quite normal to apply them to situations we have not directly experienced. The act of genius is to realise precisely where it is that we are going too far.*’ Where nowadays are we making the same sort of error as that to which Maxwell drew attention in electromagnetism?
*The quotation is taken from ‘An Introduction to the Meaning and Structure of Physics’, by Leon N Cooper, Harper and Row, NY, 1968.”
Grant and Phillips suggest such errors in other subjects, not in Electromagnetism, which as we all know has now reached perfection.
How unkind of Catt to draw attention to a further error, this time by Maxwell, in exactly the area where Maxwell supposedly pointed out an error and so supposedly created perfection, later called “Maxwell’s Equations”. Actually, Maxwell’s “solution” is bogus, because he did not know that the signal travels between the capacitor plates, at right angles to the direction that he thought it took.
Ivor Catt 25oct03
"Fields and Waves in Modern Radio" by S Ramo and J R Whinnery, 2nd ed., pub. Wiley 1953, p182;
"Total displacenemt current flowing between the plates in the area of the plate multiplied by the density of displacement current."
"Electromagnetic Waves" by S A Schelkunoff (Bell Labs), pub. Van Nostrand 1943/4, p63 Figure 4.1 is a diagram with uniform electric field between the capacitor plates. " .... electric field between the plates is nearly uniform except near the edges .... " - referring to fringing effects.
The significance of this document
This document demonstrates convincingly that nobody considered the problem of how electric charge entering a capacitor plate at one point was suddenly uniformly spread over the surface of the plate. Maxwell, textbook writers and everyone else did not merely ignore the spreading out of the charge as a simplification. They betrayed their ignorance when they gratuitously stated, or implied, that the charge on a capacitor plate was uniform.
With less disastrous results, the whole profession has been misled by the traditional, misleading way of drawing a battery as in Figure 31 in http://www.ivorcatt.com/2_4.htm , as I noticed after a century. The reality is as in Figure 33.
The whole profession has been misled by the traditional, misleading way of drawing a capacitor as in Figure 26 in http://www.ivorcatt.com/2_2.htm . This led to nobody for a whole century (until my co-author Malcolm Davidson) noticing the absurdity of the fashionable model for a transmission line, modelling a transmission line in terms of itself, see http://www.ivorcatt.com/2_2.htm figures 26, 27. A transmission line is identical to the real capacitor as drawn in Figure 27.
The third, and worst, disaster was the effect on Maxwell and his galaxy of sycophants, resulting in Maxwell’s so-called “leap of genius” (according to Heaviside) in inventing “Displacement Current”, which would have been unnecessary had he (or Heaviside, who had a much better chance) thought of drawing a capacitor more clearly, with wires attached to one end rather than to the centre.
Ivor Catt 30oct03