Why is the sky blue?
The electric field of light effects a Lorentz force
on the electron cloud ( is the charge of field of light oscillates over time
the electron cloud and
is the electric field). The electric
is the amplitude of the wave and
is the angular frequency of the incident light and its electric
field. So
The damping force is introduced pheno oscillating dipole. This damping force is actually called the radiative reaction force.
menologically to account for the radiation of energy by the
207 It is
proportional to the jerk, the third time derivative of the displacement of the electron cloud. If the electron cloud undergoes harmonic motion, the jerk can be modeled to be proportional to the velocity. It will be shown that the electron cloud undergoes harmonic motion and the reader need not worry that this assumption is not mathematically justified. So, 208
(3)
The solution to the differential equation is made up of a ‘complementary solution’ plus a ‘particular solution’. The possible complementary solutions that could result from different strengths of damping are (A and B are arbitrary co (a) nstants)
(b)
(c)
But as time tends to infinity x tends to 0 i.e. they are transient. Therefore, the long term properties of the system are determined by the particular solution, the ‘steady state solution’. It is known mathematically that the particular solution
(3)
fits the second order differential equation above. Substituting into the left hand side of (2) gives
207 Lipson, S. G., and H. Lipson. ‘13.1.1 The classical atom.’ Optical P 70. Print.
hysics. London: Cambridge U.P., 1969. 469 -
208 McDonald, Kirk T. ‘The Radiation Reaction Force and the Radiation Resistance of Small Antennas.’ Physics Examples and Other Pedagogic Diversions by K. McDonald. Princeton University, 15 Oct. 2007. Web.
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