Interaction of Multiple Electrons

We have learned how the disturbance travel time between electrons provides a short time interval during which the accelerated electron can move closer to, or further away from its neighbours, before being affected. We will take advantage of this knowledge for studying the interaction between electrons. The momentum conservation and relativistic principles outlined earlier will be imposed on them. We will also make the assumption that the initial acceleration is reproduced when the disturbance reaches the resting electron as discussed in the Thinking Aid.

First we will start with just three electrons to get a direct linkage to the preceding animations. Actuate the link and note three yellow balls symbolizing the electrons. Adjacent to them are three orange balls representing positive atoms which neutralize the whole structure. The control panel on the left is designed to allow three states of the central electron. Forward, Backward or Stop. The dots inside the circles indicate the chosen state. Note that the simulation continues regardless of the state of the control panel. The simulation itself can, as in all previous dynamic presentations, be stopped and resumed by clicking inside the window. So, if you want to freeze the action for contemplating the current state, click inside the window. If you want to change the motion of the central electron use the control panel. Prompts are provided to prevent a possible stalemate.

Whenever the central electron is accelerated or stopped it sends out a disturbance, that propagates in all direction. We display only the horizontal emissions in the form of a green arrow for acceleration and a red arrow for deceleration. The arrows point in the direction of the force, that would be exerted on another electron upon encounter.

Click the Fwd control and then start the simulation. Wait until the central electron has moved about halfway between two atoms, then click inside the window to freeze the state. By that time the accelerating green arrows have reached the adjacent two electrons and have forced them into motion. All the while, the central electron has moved closer to the one on the right and has distanced itself from the one on the left. Click inside the window again to resume the simulation and then quickly click the Stop control in the panel. A decelerating field is emitted this time in the form of two red arrows. The outer two electrons continue to move until caught up by the decelerating force. The spacing of electrons has been restored to the original. Repeat the experiment if not successful the first time.

Allow the fields to propagate outside the window boundaries and then actuate the backward control Bwd. Let the central electron travel to near its original position and then stop the simulation by clicking inside the window. Note that this time the electron spacing on the left is smaller than that of the atoms, while the electron spacing to the right is larger. This is opposite to what we noted before and it is quite obvious that the electrons tend to condense in the direction of initial acceleration. Furthermore, the net charge in the region of denser electrons is negative while it is positive in the region of rarefied electrons. This explains why a wire becomes negative or positive and how the imposition of the finite and constant propagation velocity of the force fields produces this side effect. Because the condensation and rarefaction occur in the rhythm of disturbance propagation, the negative or positive charge front progresses at the velocity of light. But the electrons themselves trail behind very slowly. Yet, wherever they are moving there is a current flowing. Consequently a current front also propagates down the wire at the speed of light.

This simulation exaggerates the typical electron speed in wires by about 12 orders of magnitude in order to make the effects discernible. Nevertheless, they are valid at any speed of electrons and explain the often puzzling question of how it is possible that the charge and current front in the wire progress at the speed of light while the electrons are almost standing still. The finite field propagation delay is therefore crucial for understanding the current flow in conductors and the experimentation with this simple model should be helpful in understanding the consequences. The reader is therefore encouraged to experiment some more and to associate our speculations about the gaps and folds with the directions of arrows used in the simulation. They all convey the existence of some force fields that are otherwise difficult to visualize. Pay attention to the fact that a direction change of electron motion consists of a deceleration followed by an acceleration in the other direction. Therefore both arrows are shown in such cases. You may let the simulation run continously and alternately click the Fwd, Bwd or Stop buttons as many times as you like and observe the plethora of motions being reproduced by the neighbouring electrons. The forward and backward controls are frozen for short time intervals in order to prevent nonphysical changes of electron motions.

Easier to visualize than the force fields is the existence of more electrons to the left and to the right of the three shown in our simulation. As encountered by the accelerating and decelerating fields they would all experience the same fate as the two we have studied so far. The effects would be simply duplicated to the left and to the right of them.

After you are comfortable with the concepts illustrated by this simulation quit it and move on to the section Barrier to Electron Motion which addresses the question of what happens to the disturbances when they reach electrons whose motion is obstructed.