ELECTRODYNAMICS
PROBLEM SET 4
due February 23
th
, before class
Problem 1.: Hidden momentum
In the discussion of the energy flow in a coaxial cable in class we argue that the Poynting vector was nonvanishing
inside the cable and pointed from the battery to the resistor.
Since the momentum of the electromagnetic field is
proportional to the Poynting vector, this result implies that the momentum of the electromagnetic fields is not zero.
Since the total momentum of the charges in motion seem to be zero, this result would imply that the total momentum
of the system is zero. For a static system, this is very odd ...
It turns out that the total mechanical momentum of the charges is not zero.
In fact, it exactly cancels the
electromagnetic one so the total momentum of the system is zero after all. The origin of this “hidden momentum” is
a subtle relativistic effect so, instead of calculating it for the coaxial cable, we will use a simpler geometry.
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 Spring '11
 Bedaque
 Energy, Momentum, Work, Electric charge, Fundamental physics concepts, Coaxial cable, Axial multipole moments, Multipole expansion

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