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(21) |
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(22) |
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(23) |
The boundary conditions determine the coefficients :
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(24) |
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(25) |
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(26) |
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(27) |
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(28) |
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(29) |
(b) Since
, the wave equation becomes
.
(c) From (b), the dispersion is obtained as
. If
you expand this to the first order in
, you obtain
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(30) |
Since is the factor that exhibits the anomalous
dispersion, the correction term to the absorption coefficient will
still show the anomalous dispersion in such a conductor.
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(31) |
(b) The electric field at the solenoid surface satisfies
, and the magnetic fiels at the axis of the ring is
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(32) |
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(33) |
(b)
where
. Time-averaged,
.
(c) The radiation damping force is
. If you take the time integral of
, then you
obtain
. In other words, the energy loss of the particle due
to the damping is the radiated power.