(a) Critique Hertz comment that Maxwell\'s theory is Maxwells Equations. Is some
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Question
(a) Critique Hertz comment that Maxwell's theory is Maxwells Equations. Is something deep being revealed here? Or is this a throwaway comment? To what are we committing ourselves if we agree with Hertz? (b) You may always orient your coordinates so that the propagation of a disturbance or wave form in empty space is along a rectangular Cartesian axis. Designating this axis to be z the general equation to be satisfied by the electric or magnetic fields, which we designate here generally as f, of an electromagnetic wave form in empty space is 1/c^2 partial differential^2 f/partial differential t^2 - partial differential^2 f/partial differential z^2 = 0. a) Show that this wave equation is satisfied by any arbitrary f = f(p) where p = (omega t + kz) and an arbitrary function provided c = plusminus omega/k. b) In the laboratory you have an electronic flashlamp that produces a flash of very short duration, which you collimate to produce a directed pulse. You assume that the shape of the pulse is Gaussian, i.e. f = K exp (-t^2/tau^2), at the location of the lamp. Does your result in part (a) indicate that this pulse will propagate to the target in your laboratory?Explanation / Answer
Solution 3(a)
Critique Hertz commented that Maxwell's theory is Maxwell's equation. Yes there lies a deep thought in this comment. It is not just a simple throwaway comment. For answering this question we have look in to past at the time of Maxwell and Hertz.
Maxwell was deeply impressed by Faraday's idea of lines of force. As a trained mathematician Maxwell was able to do what Faraday could not. Maxwell's placed Faraday's idea on firm mathematical basis.
For Maxwell form of the field theory was not a primary goal. For him the field and the medium in which the existed, the aether, were the primary quantities.
We can lookin to following points he thought.
Maxwell himself was never compeletly successful at keeping the fields primary and the pariticles and current secondary.
With time Maxwell developed his famous sets of equation.
Hertz performed the experiments to realize the Maxwell's equation. But it was the difficulty in interpreting Maxwell and his idea about aether from his sets of equation which made him to make this comment.
According to Hertz "Maxwell's idea has caused mant to abandon the hope of forming ..an altogether consistent conception of Maxwell's idea".
He further commented that Maxwell's theory is only a Maxwell's set of equations. It is not Maxwell's particular conception or method.
Maxwell's equation are always useful but its interpretation was never done as described by Maxwell.
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