Question

The magnetic component of an electromagnetic wave in vacuum has an amplitude of 95.2 nT and an angular wave number of 1.72 m-1. What are (a) the frequency of the wave, (b) the rms value of the electric component, and (c) the intensity of the light?

Answer 1

Answer:

82123950.63541 Hz

20.19496 V/m

1.08181 W/m²

Explanation:

c = Speed of light = $3\times 10^8\ m/s$

$\mu_0$ = Vacuum permeability = $4\pi \times 10^{-7}\ H/m$

$\lambda$ = Wavelength

f = Frequency

B = Magnetic field = 95.2 nT

Wave number is given by

$k=\frac{2\pi}{\lambda}$

$\lambda=\frac{c}{f}$

$\\\Rightarrow k=\frac{2\pi}{\frac{c}{f}}\\\Rightarrow f=\frac{ck}{2\pi}\\\Rightarrow f=\frac{3\times 10^8\times 1.72}{2\pi}\\\Rightarrow f=82123950.63541\ Hz$

The frequency of the wave is 82123950.63541 Hz

Electric field is given by

$E_a=B_ac\\\Rightarrow E_a=95.2\times 10^{-9}\times 3\times 10^8\\\Rightarrow E_a=28.56\ V/m$

RMS of electric component is given by

$E_r=\frac{E_a}{\sqrt2}\\\Rightarrow E_r=\frac{28.56}{\sqrt2}\\\Rightarrow E_r=20.19496\ V/m$

The rms value of the electric component is 20.19496 V/m

Average intensity of light is given by

$I=\frac{E_r^2}{c\mu_0}\\\Rightarrow I=\frac{20.19496^2}{3\times 10^8\times 4\pi\times 10^{-7}}\\\Rightarrow I=1.08181\ W/m^2$

The intensity of the light is 1.08181 W/m²