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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»

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}


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