Allegedly uniform field in a capacitor

 

“The field E of such a capacitor is uniform between the plates ….”

 

 

 [Paul Fishbane, P M Fishbane, Stephen Gasiorowicz, S Gasiorowicz, Stephen Thornton, S T Thronton]

"Physics for Scientists and Engineers …." By Paul M Fishbane, University of Virginia; Stephen Gasiorowicz, University of Minnesota; Stephen T Thornton, University of Virginia, pub. Prentice-Hall 1996, 1993

 

p826 The Maxwell Displacement Current

There is a logical flaw in Ampere's law when there is a time dependence in the current.

…. When the current deposits charge on the plates of a capacitor.

….

 

P827 The field E of such a capacitor is uniform between the plates ….

Figure 30-30 has a uniform field

 

P828 …. The electric field is constant ….


It is permissible to point out "a logical flaw in Ampere's law", because Maxwell's career is over, and his pension in not under threat. The same does not apply to logical flaws in the writings of Fishbane, Gas and Thornton. The logical flaw which I point out, that they have omitted to consider whether, "when the current deposits charge on the plates of a capacitor", it causes a magnetic field as it travels across the plate from the input lead in order to make "The field E of such a capacitor …. uniform between the plates".

 

Of course, should they listen to me, and actually hear that electric charge/current entering the capacitor plate then travels at right angles across the plate, they would have to (1) consider whether Maxwell and Heaviside realised that, and (2) whether displacement current still serves a purpose. [The lateral current satisfies Gauss's Law without any leap of Maxwell genius, Displacement Current.] If not, they would have to do something about the section's title; The Maxwell Displacement Current

Ivor Catt  11nov03

 

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The significance of this document

 

1

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.

 

2

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