To solve this problem, it is necessary to apply the concepts related to the electric field according to the intensity of the wave, the permittivity constant in free space and the speed of light.
As well as the expression of the rms of the magnetic field as a function of the electric field and the speed of light.
PART A) The expression for the rms of electric field is
[tex]E_{rms} = \sqrt{\frac{S}{\epsilon_0 c}}[/tex]
Where,
S= Intensity of the wave
[tex]\epsilon_0[/tex]= Permitivitty at free space
c = Light speed
Replacing we have that,
[tex]E_{rms} = \sqrt{\frac{(2.93*10^9)}{(8.85*10^{-12})(3*10^8)}}[/tex]
[tex]E_{rms} = 1.05*10^6N/C[/tex]
The RMS value of electric field is [tex]1.05*10^6N/C[/tex]
PART B) The expression for the RMS of magnetic field is,
[tex]B_{rms} = \frac{E_{rms}}{c}\\B_{rms} = \frac{1.05*10^6}{3*10^8}\\B_{rms} =3.5*10^{-3}T[/tex]
The RMS of the magnetic field is [tex]3.5*10^{-3}T[/tex]
A. The rms value of electric field be "1.05 × 10⁶ N/C".
B. The rms value of magnetic field will be "3.5 × 10⁻³ T".
According to the question,
Intensity of the wave, S = 2.93 × 10⁹ W/m²
Free space permittivity, [tex]\epsilon_0[/tex] = 8.86 × 10⁻¹²
Speed of light, c = 3 × 10⁸
A. We know that,
The rms value of electric field,
→ [tex]E_{rms}[/tex] = [tex]\sqrt{\frac{S}{\epsilon_0 c} }[/tex]
By substituting the values,
= [tex]\sqrt{\frac{2.93\times 10^9}{(8.85\times 10^{-12})(3\times 10^8)} }[/tex]
= 1.05 × 10⁶ N/C
and,
B. We know that,
The rms value of magnetic field,
→ [tex]B_{rms}[/tex] = [tex]\frac{E_{rms}}{c}[/tex]
By substituting the values,
= [tex]\frac{1.05\times 10^6}{3\times 10^8}[/tex]
= 3.5 × 10⁻³ T
Thus the above response is appropriate.
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