[2013EM/HMW-12]

PHY 102: Introduction to Physics-2
Tutorial-12
(Electromagnetic waves)

1. Electromagnetic wave: The electric fields of two harmonic electromagnetic waves of angular frequency $\omega_1$ and $\omega_2$ are given by $\vec{\pmb E}_1(x,t)=E_{1,0}\cos(k_1x-\omega_1 t)\hat{\pmb j}$ and by $\vec{\pmb E}_2(x,t)=E_{2,0}\cos(k_2x-\omega_2t+\delta)\hat{\pmb j}$. For the resultant of these two waves, find (a) the instantaneous Poynting vector and (b) the time-averaged Poynting vector. (c) Repeat parts (a) and (b) if the directi9on of propagation of the second wave is reversed so that $\vec{\pmb E}_2(x,t)=E_{2,0}\cos(k_2x+\omega_2t+\delta)\hat{\pmb j}$.
2. Electromagnetic waves in a conducting medium:  (a)~Calculate the penetration depth for 2 MHz electromagnetic (EM) wave through copper, $\sigma=5.8\times 10^7$ mho/m.\\ (b)~For silver, $\sigma=3.0$ MS/m., Calculate the frequency at which the depth of penetration is 1 mm. [$\mu_r=1$]\\ (Given $\mu=4\pi\times10^{-7}$Henry/m, $\epsilon_0=8.854\times10^{-12}$F/m)
3. Electromagnetic wave: A uniform plane wave propagating in a medium has ${\pmb E}=2e^{-\alpha\cdot z}\sin(10^8t-{\pmb\beta} z){\pmb a}_y$V/m. If the medium is characterized by $\epsilon_r=1$, $\mu_r=20$, and $\sigma=3$ mhos/m, find real, imaginary part of wave vector and screen depth.