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

82123950.63541 Hz

20.19496 V/m

1.08181 W/m²

Step-by-step explanation:

c = Speed of light =
`3* 10^8\ m/s`

`\mu_0` = Vacuum permeability =
`4\pi * 10^(-7)\ H/m`

`\lambda` = Wavelength

f = Frequency

B = Magnetic field = 95.2 nT

Wave number is given by

`k=(2\pi)/(\lambda)`

`\lambda=(c)/(f)`

`\\\Rightarrow k=(2\pi)/((c)/(f))\\\Rightarrow f=(ck)/(2\pi)\\\Rightarrow f=(3* 10^8* 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* 10^(-9)* 3* 10^8\\\Rightarrow E_a=28.56\ V/m`

RMS of electric component is given by

`E_r=(E_a)/(\sqrt2)\\\Rightarrow E_r=(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=(E_r^2)/(c\mu_0)\\\Rightarrow I=(20.19496^2)/(3* 10^8* 4\pi* 10^(-7))\\\Rightarrow I=1.08181\ W/m^2`

The intensity of the light is 1.08181 W/m²