Question

Question 8.8: Suppose that the electric field amplitude of an electromagnetic wave is E0 = 120 N/C and that its frequency is ν = 50.0 MHz. (a) Determine, B0, ω, k, and λ. (b) Find expressions for E and B.

Class 12 - Physics - Electromagnetic Waves Electromagnetic Waves Page-286

Answer 1

Given,
electric field amplitude , $E_0$=120N/C
frequency of source, $\nu$=50MHz
speed of light , c = 3 × 10^8 m/s
(a) magnitude of magnetic field Strength is given as $B_0=\frac{E_0}{c}=\frac{120}{3\times10^8}\\B_0=4\times10^{-7}T$
Angular frequency of the source is given as
$\omega=2\pi\nu=2\pi\times50\times10^6rad/s$
propagation constant is given as $\kappa=\frac{\omega}{c}$
k = 3.14 × 10^8/3 × 10^8 = 1.05 rad/m
now, wavelength of wave is given as $\lambda=\frac{c}{\nu}$
$\lambda$ = 3 × 10^8/5 × 10^7 = 6 m


(b) suppose the wave is propagating in positive x direction.then electric field vector will be in the positive y direction and the magnetic field vector will be positive z direction. this is because all the planes are mutually perpendicular to each other.
equation of electric field vector is given as
$E=E_0sin(kx-\omega t)\hat{i}\\E=120sin(1.05x-3.14\times10^8t)\hat{i}$

and magnetic field vector is given as
$B=B_0sin(kx-\omega t)\hat{k}\\B=4\times10^{-7}sin(1.05x-3.14\times10^8t)\hat{k}$