Traditionally. when a TEM step (i.e. logic transition from low to high) ( Figures 3, 4, 5 from Electromagnetism 1 ) travels through a vacuum from left to right, guided by two conductors (the signal line and the 0v line), there are four factors which make up the wave;
- electric current in the conductors i
- magnetic field, or flux, surrounding the conductors B
- electric charge on the surface of the conductors +q , -q
- electric field, or flux, in the vacuum terminating on the charge (Figure 2), D
The key to grasping the question is to concentrate on the electric charge -q on the bottom conductor. The step advances one foot per nanosecond. Extra negative charge appears on the surface of the bottom conductor to terminate the new lines (tubes) of electric flux D (figure 2) which appear between the top (signal) conductor and the bottom conductor.
1982 the question has been: Where does this new charge come from?
Sir Michael Pepper, Knighted "for services to Physics", privately writes that it comes from the south.
Nobel Prizewinner Professor Josephson privately writes that it comes from the west.
After being ignored by all peer reviewed journals for a third of a century, Massimiliano Pieraccini and Stefano Selleri published two replies, one being in this journal. They took a small section of the transmission line ∆x and discussed the charge entering and leaving it, concluding that there was no real paradox.
November 2013 PHYSICS EDUCATION 719
718 PHYSICS EDUCATION 48(6) 0031-9120/13/060718+05$33.00 c
2013 IOP Publishing Ltd
An apparent paradox: Catt’s anomaly
M Pieraccini and S Selleri
“The solution. The key idea of the explanation of this apparent paradox is related to the great number of electrons in metal. Although each single electron is not able to travel at the speed of light, a great number of slow electrons are able to produce a current as fast as an electromagnetic wave travelling at the speed of light in the conductor.”
In the race between the electrons and the TEM wave, or between the tortoise(s) and the hare, however we look at it, 100 or even 1,000 tortoises will fall further and further behind.
“This incoming current lasts for a time interval ∆t and produces in the wire length ∆x an imbalance of charge ∆Q given by ∆Q=I∆ t=I∆ x⁄ c . (2)”
“and produces in the wire length ∆x an imbalance of charge ∆Q”. This very large amount of charge is not uniformly distributed in the section ∆x. It is all concentrated at the left hand end of that section, ∆∆x, because it travelled slowly.
“After ∆t has elapsed, the current starts to ﬂow out of our sampling volume and the charges entering from the left are balanced by those escaping towards the right.”
“After ∆t has elapsed, the current starts to ﬂow out of our sampling volume” Not so, because the charge required to produce this current flowing out is far away at the left hand end of ∆x. Before it could start to flow out of the section ∆x, some of it would have to have traversed the length ∆x at the speed of light.
Ivor Catt 14 December 2015.