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Fields

In Classical Mechanics we found several conceptual aids that not only made calculations easier by skipping over inessential details but also made it possible to carry around the bare essence of Mechanics in our heads in a small number of compact "Laws." This is generally regarded as a good thing, although of course we pay a price for every entrenched paradigm - we may lose the ability (if we ever had it!) to "see things as they are" without filtering our experience through models. I will leave that debate to the philosophers, psychologists and mystics; it is true even in Physics, however, that the more successful the paradigm the bigger the blind spot it creates for alternative descriptions of the same phenomena. This bothers most Physicists, too, but there doesn't seem to be a practical alternative; so we content ourselves with maintaining an awareness of our own systematic prejudices.

Perhaps the best example of this from the days of "Classical" Physics [i.e. before Relativity and Quantum Mechanics rained confusion down on all of us] is the invention of the ELECTRIC and MAGNETIC FIELDS, written $\Vec{E}$ and $\Vec{B}$, respectively. The idea of FIELDS is to break down the nasty problems described in the previous Section into two easier parts:

1.

First, calculate the FIELD due to the source charge or current.

2.

Then calculate the force on a test charge or current due to that FIELD.

This also makes it a lot easier to organize our calculations in cases where the sources are complicated arrays of charges and/or currents. Here's how it works: