Question

(2.8)* Consider a simple Lorentz oscillator with a single undamped resonance. The dielectric constant will be given by eqn 2.14 with $x$ and $y$ both zero. This gives: \\ $\epsilon_r(\omega) = 1 + \frac{Ne^2}{\epsilon_0 m_0} \frac{1}{\omega_0^2 - \omega^2}$. \\ Prove that the group velocity is always less than $c$.

          (2.8)* Consider a simple Lorentz oscillator with a single undamped resonance. The dielectric constant will be given by eqn 2.14 with $x$ and $y$ both zero. This gives: \\
$\epsilon_r(\omega) = 1 + \frac{Ne^2}{\epsilon_0 m_0} \frac{1}{\omega_0^2 - \omega^2}$. \\
Prove that the group velocity is always less than $c$.

(2.8)* Consider a simple Lorentz oscillator with a single undamped resonance. The dielectric constant will be given by eqn 2.14 with x and y both zero. This gives:

(ω) = 1 + (Ne^2)/(ϵ0 m0)(1)/(ω0^2 - ω^2).

Prove that the group velocity is always less than c.

Added by Jean S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Prachita Kush

01/10/2022

Step 1

It can be calculated as v_g = dω/dk, where ω is the angular frequency and k is the wave number. Show more…

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(2.8)* Consider a simple Lorentz oscillator with a single undamped resonance. The dielectric constant will be given by eqn 2.14 with chi and gamma both zero. This gives: epsi lon_(r)(omega )=1+(Ne^(2))/(epsi lon_(0)m_(0))(1)/((omega _(0)^(2)-omega ^(2))). Prove that the group velocity is always less than c. 2.8* Consider a simple Lorentz oscillator with a single un damped resonance.The dielectric constant will be given by eqn 2.14 with X and y both zero.This gives: Ne2 -1- omo Prove that the group velocity is always less than c