Question

1. The Lorentz model of a dielectric material treats bound electrons as a damped harmonic oscillator. The Equation of motion for an electron is thus m d^2x/dt^2 + ? dx/dt + ?x = eE = eE_0 exp (i?t) Derive the solution to this equation in terms of the resonant frequency ?_0 = ??/m, showing that x = x_0 exp(i?t) = (eE_0 exp(i?t - i?)) / ?(m^2(?_0^2 - ?^2)^2 + ?^2?^2) and ? = tan^-1 { (??) / (m(?_0^2 - ?^2)) }

          1. The Lorentz model of a dielectric material treats bound electrons as a damped harmonic oscillator. The Equation of motion for an electron is thus
m d^2x/dt^2 + ? dx/dt + ?x = eE = eE_0 exp (i?t)
Derive the solution to this equation in terms of the resonant frequency ?_0 = ??/m, showing that
x = x_0 exp(i?t) = (eE_0 exp(i?t - i?)) / ?(m^2(?_0^2 - ?^2)^2 + ?^2?^2)
and
? = tan^-1 { (??) / (m(?_0^2 - ?^2)) }

1. The Lorentz model of a dielectric material treats bound electrons as a damped harmonic oscillator. The Equation of motion for an electron is thus
m d^2x/dt^2 + ? dx/dt + ?x = eE = eE0 exp (i?t)
Derive the solution to this equation in terms of the resonant frequency ?0 = ??/m, showing that
x = x0 exp(i?t) = (eE0 exp(i?t - i?)) / ?(m^2(?0^2 - ?^2)^2 + ?^2?^2)
and
? = tan^-1 (??) / (m(?0^2 - ?^2))

Added by Taylor G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Supreeta N

11/30/2023

Step 1

In this model, the bound electrons in the material are treated as damped harmonic oscillators. This means that they experience a restoring force that is proportional to their displacement from equilibrium, but also experience damping due to interactions with other Show more…

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The Lorentz model of a dielectric material treats bound electrons as a damped harmonic oscillator. The equation of motion for an electron is thus: showing that: and: