Barrier to Electron Motion

If an electron is at a barrier, like at the end of a wire, and receives an acceleration push it can accelerate but then it must immediately decelerate when stopped by the barrier. In the animation this process is illustrated using the color and iconic scheme introduced in the preceding simulation. The green arrowhead indicates an accelerating "fold" which will push the yellow electron against the wire end. Click the mouse button anywhere inside the animation window and watch how the deceleration of the electron, which must immediately follow the acceleration, emits deceleration disturbances. These propagate in all directions but we show only the forward and the backward components as red arrowheads. Because of the opposite polarity of the acceleration and deceleration disturbance the green and red arrowheads, travelling to the right, actually cancel each other. The reader may use our earlier speculation about gaps and folds as an aid to guessing how the two may cancel each other. The consequence is that no disturbance gets emitted out the end of the wire.

The other red deceleration component travels backwards into the wire uninhibited. In terms of our speculative thinking it is a "fold" produced by the electron bouncing backwards from the wire end. But it looks essentially like a reflection of the original fold. Should this red disturbance encounter an electron traveling at the same speed as the electron which emitted the original green disturbance this electron would be decelerated to exactly zero velocity. This animation can be repeated by clicking of the mouse button when suggested by the prompts. As in all animations, a click during the motion will stop it and the next click will resume it. Quit the animation before proceeding.

A Side Show

A more detailed insight into the behaviour of interacting electrons away and near the barriers can be obtained from the simulation which we will examine next. It consists of five electrons of which only the first one can be influenced from the control panel on the left. The familiar "Fwd", "Bwd" and "Stop" controls operate in the same way as in the simulation of three electrons. As always, the simulation can be frozen and resumed by clicking inside the window. Since we already know the direction of force on electrons exerted by the disturbances we show these only as green or red dots, depending on whether they are of accelerating or of decelerating kind, respectively.

Actuate the backward "Bwd" control and watch how the accelerating disturbance gradually produces a rarefied brigade of electrons. Freeze the simulation by clicking inside the window before the first electron reaches the left edge. A click on the "Reset" button will get you back to the starting point. Repeat the action and this time pay attention to the motion of the locus of increased spacings. While the electrons are moving to the left the locus of increased spacing is moving to the right. Reset again and repeat the same simulation but this time actuate the Stop control as soon as all five electrons are moving. The stoppage of the first electron generates a deceleration field which brings the formation to a halt one electron at a time. Note that the locus of neutrality moves again to the right. If you missed this try again.

Reset and this time actuate the control buttons in the sequence Forward, Stop, Backward, Stop, Forward, Stop and so on as fast as you can. What you observe is a stepwise modulation of electron velocities. If the spacing of atoms were representative of copper the modulation rate would be comparable to that of X-rays. The acceleration and deceleration disturbances or our speculative folds and gaps have been reproducing the modulation of the controlled electron in all other electrons. This is how the signals from a voltage or a current source get transmitted over a wire. Even though the electrons essentially stayed in place the modulation of the first electron has propagated at near the velocity of light down the wire from electron to electron. Because the folds and gaps are being reproduced along the way, their velocity is somewhat smaller than the velocity of light. You can produce more complex signals and watch how the patterns imposed are reproduced along the wire.

If you want to experiment some more with this setup you can make it less boring by actuating the "Field" button in the left control panel. This will insert a spring like structure between electrons which will be compressed or stretched in the process of electron motion. A stretched spring represents positive potential and vice versa. Once you have resolved most of the questions raised by this simulation, you can make the experimentation more interesting by speeding it up. This you can do by sliding the speed control on the bottom of the window more or all the way to the left. When you are running at full speed you may run into some difficulties with the simulation but a Reset should always restore it to the initial state.

Back On Track

We have strayed for the moment from the main object of this simulation which is to illustrate the reflections from barriers. Reset the simulation and actuate the control labeled "Barrier" in the left control panel. A boundary should appear around our display emulating the end of a wire. You may or may not have the "Field" button depressed during this experiment. In the "Barrier" state you do not get the freedom of modulating the electron velocity. The simulation runs essentially by itself once you start it. You will get two different outcomes depending on whether you start with the "Forward" or the "Backward" button. Let us start with "Forward" and observe the by now familiar compression take place. Note that the electron formation is tightening up from left to right. As the end of the wire is reached the red deceleration disturbance is created which travels backward and stops the formation but not before the electrons have had the chance to close in on each other even more. Note that this time the tightening takes place from right to left. We have thus first observed a locus of net negative charge traveling to the right and now a locus of an even more negative net charge traveling to the left. Of course, none of the electrons have ever been moving to the left in the process.

Actuate now the "Backward" control and observe the spreading out of electrons beginning at the left and progressing to the right. As the disturbance reaches the last electron it is reversed by it. The deceleration is now catching up with the departing electrons which succeed to separate even more before they are stopped. But the additional rarefaction is now starting at the barrier and is moving to the left. Because a rarefaction of electrons represents a net positive charge we observed first a positive net charge traveling to the right and then one even more positive net charge traveling to the left.

Both cases that we have examined, are reminiscent of behaviour in open ended transmission lines which exhibit a potential travelling from the source to the load, doubling at the open end and then travelling as such towards the source. A detailed analysis shows that in our simulation the net charge exactly doubles when the final spacings are attained. The potential is proportional to the net charge for a uniform transmission line. The net charge is always proportional to the difference of inverse atom spacings and the inverse electron spacings, the two representing their respective densities. Consequently, the potential can be represented as this difference. We will take advantage of this fact in later presentations.

You may want to repeat these simulations to firm up the foundation necessary for understanding the quarter wave resonance in open-ended wires. Anytime during the simulation you may arrest and resume the progress by clicks inside the window. When you are done experimenting, quit the simulation and move on to the section Terminated Wires in which we will vividly illustrate the necessity of having different velocities in the positive and negative wires and for that matter on the two terminals of voltage sources.