||A few concepts
In order to completely understand EM interactions we
need to go beyond the simple picture given to us by Coulombís law.
Coulombís law gives us an action at a distance model.
It implies that the instant we move one charge another charge would feel
the effects. Each charge acts directly on the other charges.
Why is this bad? Well, it would give us infinitely quick information
propagation and this does not happen.
So, Coulombís law is fine for charges at rest (which
is what we're doing here), but when we start to deal with moving charges,
we'll need to modify it.
There must be something which actually exerts the force
on charges. This is where the idea of a field comes into play.
Let's go back to gravity for a moment... What is actually
pulling you toward the surface of the earth? Is the earth reaching
up with a hand and pulling you down? Of course not. There must
be something which exerts the force, and it is the gravitational field
that the earth creates.
The field model gives us the picture of having the space
which surrounds a charged particle being filled with an electric field.
Unlike a point charge, it occupies all of space simultaneously.
A field (whether it is gravitational, electric or magnetic)
is very real, it has momentum and energy just like particles.
The previous (incorrect) picture was
Our new picture for how the particles interact is
The information of a wiggling charged particle is now
propagated through the field at the speed of light. You can (sort
of) think of this interaction like ripples on a pons surface spreading
Fields can be difficult to comprehend, but they are
the cornerstone of this semester.
Now we can move on to more quantitative description
of electric fields.