[2013EM/HMW-11]

PHY 102: Introduction to Physics-2
Tutorial-11
(Electromagnetic waves)

1. Electromagnetic wave: Following equation contains the complete information about the electromagnetic wave: $$ \vec{\pmb E}(z,t)=E_0\sin(kz-\omega t)\hat{i} $$ Find the directions of wave propagation, wavelength, frequency, speed of propagation, magnetic field $\vec{\pmb B}$, the Poynting vectors $\vec{\pmb S}$ and the intensity of the wave.
2. Solar constant: At the upper surface of the Earth's atmosphere, the time-averaged magnitude of the Poynting vector, $=1.35\times 10$ W/m$^2$, is referred to as the solar constant.
   1. [(a)] Assuming that the Sun's electromagnetic radiation is a plane sinusoidal wave, what are the magnitudes of the electric and magnetic field?
   2. [(b)] What is the total time-averaged power radiated by the Sun? The mean Sun-Earth distance is $R=1.50\times10^{11}$m.
3. Electromagnetic wave: An electromagnetic plane wave has an electric field that is parallel to the $y$ axis, and has a Poynting vector that is given by, $$ \vec{\pmb S}(x,t)=\left(100{w\over m^2}\right)cos^2(kx-\omega t)\hat{\pmb i} $$ where $x$ is in meters, $k=10.0$ rad/m, $\omega=3.00\times10^9$ rad/s, and $t$ is in seconds. (a) What is the direction of propagation of the wave? (b) Find the wavelength and frequency of the wave. (c) Find the electric and magnetic fields of the wave as functions of $x$ and $t$.