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Explaining



Well, I've had many undergraduates who will respond to a question testing
this concept, saying that they believe that resistors heat up because the
electrons lose kinetic energy when passing through the resistor, which is
the same as saying they go in faster than they come out. I would have
thought they'd not respond this way if they really grasped the continuity
equation, or Kirchoff's laws.

Then, later on, you hit 'em with the Poynting's flux "explanation"!
This is one of the very clear examples of our being able to describe
Nature without really being able to explain it. If you can't even
tell me where the energy comes from (either in through the wires as
potential energy loss from charges falling in the electric field or
in from infinity at the speed of light with ExB intensity) then how
can you believe you can explain this phenomenon?

We describe; we don't explain. Our descriptions have a coherent
mathematical consistency that confers upon our descriptions a
predictive value. We delude ourselves if we think we can explain
anything in a fundamental sense; we merely know how to manipulate
rules (laws) to achieve reliable predictions.

Why are all electrons the same? We don't know. We can't derive that
result, or explain it. It has become one of those rules we use to
explain other things. The observation that all electrons are
identical has become one of the rules we use to construct consistent
decriptions of Nature.

Leigh