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2C: Electromagnetism
in Relativity & in Dense Matter
Feynman
Simplified 2C covers one
quarter of
Volume 2, the freshman course, of The Feynman Lectures
on Physics. The topics we explore include:
- Relativistic Maxwell’s Equations
- Lorentz Transform for Potentials & Fields
- Field Energy, Momentum & Mass
- Relativistic Particles in Fields
- Crystals
- Refraction & Reflection in Dense Matter
- Waveguides
Excerpt:
Energy of Fields
We
want now to quantitatively analyze the energy of electromagnetic fields
in various circumstances. To do this, we need to quantify energy
density and energy flow. We define u to be the electromagnetic field
energy density per unit volume, and S to be the energy flow vector, the
amount of energy per unit time per unit area passing through a surface
perpendicular to S.
In V2p27-2,
Feynman says: “in perfect analogy with the conservation of charge, we
can write the ‘local’ law of [field] energy conservation” as:
∂u/∂t + Ď•S = 0
This
equation is valid when the energy of the electromagnetic field is
conserved, which it is not in general. Total energy of all types is
locally conserved, but energy freely changes from one type to another.
Feynman gives the example of walking into a dark room and switching on
the lights; field energy suddenly increases, while the energy of the
power grid decreases.
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