Electrostatics
Electrostatics deals with charges as if they were already there. In truth, the only system that preexists with charges are atoms, and what goes inside the atom stays inside the atom. So, all charges are brought (or accelerated) near other charges for these laws to work. As we shall go on to learn that accelerated charges produce electromagnetic waves, Electrostatics essentially ignores these movements and the electromagnetic waves, and gives laws for what shall happen if the charges were suddenly at those places in the system. Electrostatics simply creates a framework for working inside the laws observed in our universe and allows us to see what happens in various situations where it doesn’t matter a lot whether the charges were already there or were brought there whence some work was done on them.
In this chapter we will talk about how motion of charges produces forces in other charges, and about the pros and cons of fields in physics.
Table of Contents
How do Electrostatic Forces Work?
The above video showed how a charge moving in the x direction produces an EM wave in the same direction and affects another charge. You might have read that electromagnetic waves travel perpendicular to both electric and magnetic fields. This is only half the picture. Although the wave propagates perpendicular to both electric and magnetic fields, its wavefront covers all possible directions. So in essence, every charged particle that accelerates produces a wave in all possible directions. The following GIF shows how that looks like in 2D. The lines shown are field lines.
This is how any charge anywhere knows that another charge’s electric field has changed: through electromagentic waves.
The Notion of Fields in Physics
Although there is no evidence for the presence of any kinds of fields permeating all of the universe, scientists believe that fields are more than just mathematical constructs used to calculate forces due to particle systems. However, there are many problems to the theory of an all permeating field that scientists choose to ignore while working with fields.
Problems With the Theory of Fields
- While working with the mathematics of fields in the Maxwell realm, one has the option of going against causality, saying that charge which is acted upon by the movement of the source charge might experience the wave before the source itself experiences it. However, the field theory assumes the opposite just because it explains causality.
- While describing the motion of an accelerated charge, the above assumption has to be broken and the option to operate under a world not following causality has to be considered anyway.
- Since charges radiate when accelerated, they lose energy. Since they lose energy, they get slower (i.e. accelerate again) and will theoretically lose energy again until they come to a stop. However, as we know, charges don’t have a fixed position, hence they must not stop. The mathematical solution for this is that they attain constant velocity, and mathematically in doing so, they would need to know their final velocity before they have been accelerated, which again contradicts causality.
Source: Hoyle & Narlikar ’94, Cosmology and Action at a Distance Electrodynamics
Action at a distance
The opposite of field theory, AAAD theory suggests that there is nothing all permeating in the universe and charges exert forces on each other because they can. Although a bit tougher mathematically, action at a distance does not have any problems when it comes to explaining electrodynamics, that fields do (It does meet some resistance when related with gravity and cosmology). However, scientists have preferred using fields because they think that energy cannot travel without a medium, and it is generally more acceptable to think of electromagnetic fields as that medium. For further reading on this refer to Hoyle & Narlikar, and Woodward’s Gravitational Absorber Theory.