The magnetic component of an electromagnetic wave in vacuum has an amplitude of 104 nT and an angular wave number of 1.66 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

a)Frequency=  7.9 x 10 ^7Hz

b)Rms value of electric field=22.065 V/m

c) Intensity of light =1.291W/m²

Explanation:

a) Frequency of wave

first, The Angular wave number k is calculated as 2π/λ( wavelength)

and Wave number = 1.66 m -1

Wavelength =   2π/k

         = 2(3.142) /1.66

           =3.786m

Therefore Frequency f = c/λ

             =3 x10^8 /3.786

                 = 79,239,303Hz = 7.9 x 10 ^7Hz

b) The RMS of electric component

First, we find The amplitude of the  electric field,  E = c B  

where the  Amplitude of the magnetic field, B  =  104nT =104 x10 -9 T

  = 3 x10^8 x 104 x10 -9 )

=31.2V/m

Rms value of electric field E rms = E /

      = 31.2 / 1.414

      = 22.065 V/m

C) Intensity of light = (E rms)² / μ₀c

μ₀=magnetic permeability of free space, 4π x 10^-7N/A²

c= speed of light = 3x 10^8m/s

=(22.065)²/ 4π x 10^-7 x 3x 10^8m/s

=1.291W/m²

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y

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