The Catt Question
“’Electricity’ is the last of the medaeval fluids. Its downfall came when mass was attributed to it.” —Ivor Catt,
"The Catt Question" is in regard to a two-wire transmission line in conventional electromagnetic theory (Theory N). See figures 1, 2, and 3 at http://www.ivorcatt.com/1_1.htm
The wires may be any length, as the load at the other end does not enter into the Question. We are looking at the time period between the closing of the two switches of Figure 3, and before the 'electricity' can reach the load. Notice that a battery and two wires are a two-wire transmission line.
Two switches are used simply to make the visualization easier. When the (DPST) switches are closed, 'electricity' from the battery will move at the speed of light toward the right. A 'current', 'i', moves in one direction on one wire. An equal and opposite electric current, '-i', moves the other direction, according to Figure 1. These each cause magnetic fields to encircle the wires as shown.
Behind this transient electricity wavefront, we measure a voltage, equal to the battery voltage, under Theory N. To right of the wavefront there is no voltage difference (assume the wires were e.g. previously grounded or whatever). Therefore, there is an electric field, expressed either as flux, or strength, or displacement, between the two wires to the left of the wavefront. This is shown in Figure 1 as the arrows marked 'D' (for displacement). The feet of the arrows terminate on the positive charges, '+q', on the upper wire. The heads of the arrows terminate on the negative charges, '-q', on the lower wire. This is standard practice. Figure 2 is a qualitative end-view of the electric field of Figure 1, behind the wavefront. Notice in particular, that is does not matter what the ramp-up profile of the wavefront was- maybe it's a step, or a triangle, or something else. In all cases, we will see instantaneous fields as in Figure 2, at each point along the wires in Figure 1.
In order for this transverse electric field to exist, there has to be an excess of negative electric charge transported toward the battery on the upper wire, and an excess of negative charge transported toward the wavefront on the lower wire. Otherwise, there would not be any possible voltage difference between the two wires.
The Catt Question:
Where does the negative charge come from on the lower wire?
Some net-something has to move at the speed of light, or else something has to violate Gauss.