Ordinary, electrically neutral matter
Suppose that an electron would feel individually the inertia caused by the fields of electrons and nuclei in a nearby lump of matter, and one could sum these amounts of inertia to get the total inertia. We calculated the inertia in our March 31, 2023 post.
Then that lump of matter would increase the inertia of an electron enormously. This does not happen.
Rule 1. If we have many charges of opposite signs, then we can calculate the sum of the fields, and the inertia of a test charge is determined by the sum.
If we use neutral matter as a test object, then the following probably holds:
Rule 2. The inertia of a group of opposite charges in an electric field can be calculated from the sum of the fields of individual charges.
These hold for neutral matter. But we are not sure if they hold for a group of charges which have the same sign.
|| ● +
|| ● +
|| ● +
+ - --->
layers of negative positive charges
and positive charge
attached to each other
Suppose then that we have thin layers of positive and negative charge moving in an electric field, as in the diagram. The positive charges pull the negative layer, that is, give energy to its movement.
If the energy to the negative layer would be shipped from far away, then there would be significant extra inertia. But the double layer is quite similar to neutral matter: the only difference is that the charges are ordered in layers. We do not believe that there is much extra inertia.
Rule 3. We conclude that the energy to the negative layer must be shipped from very close, from the adjacent electric field just right from the layer.
We have suspected that there might be extra inertia associated with the low potential of the negative layer in the field of the positive charges. Our reasoning with the double layer suggests that it is not the case. There is no extra inertia when we move the double layer, even though the negative layer is in a low potential and the positive layer in a high potential.
Rule 4. The extra inertia seems to be associated only with energy flow in the electromagnetic field.
A spherical shell of negative charge collapses on a positive charge
We can now analyze our perennial problem of the inertia of a collapsing shell of charge.
-
_____
/ \
- | ●+ | -
\______/
-
The shell is negatively charged. We have suspected that when the shell contracts, there is extra inertia from two sources:
1. The potential of the shell is low. The shell might ship "negative energy" from one place to another.
2. The shell harvests energy from the field of the positive charge and gains kinetic energy. The harvested energy might not come from the adjacent field but from remote locations. Then there would be a lot of energy shipping and extra inertia.
Rule 4 says that item 1 does not contribute extra inertia. No energy flows in the electric field when we lower the shell.
Rule 3 says that the kinetic energy is shipped from the adjacent field. There is no extra inertia.
Conclusions
We used examples consisting of neutral matter to analyze extra inertia within an electric field. We believe that neutral matter does not feel any extra inertia. Our conclusion is that energy flow in the electromagnetic field determines the extra inertia.
Furthermore, if a layer of charge moves, the layer harvests its kinetic energy from the adjacent field. There is no extra inertia in that process.
When a poinlike test charge moves within an electric field, the situation is wholly different. The Poynting vector says that energy flows in the electromagnetic field.
Spherical shells, in a sense, are electromagnetism in one spatial dimension. It is quite different from a pointlike test charge in three spatial dimensions.
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