Respuesta :
Answer:
(a) Average energy density is 4.67 × 10⁻⁶ J/m³
(b) The rms value of the electric field is 726.26 V/m
and the rms value of the magnetic field 2.42 × 10⁻⁶ T
Explanation:
The average energy density < u > is given by
< u > = I / c
Where I is the intensity and
c is the speed of light
From the question
I = 1400 W/m²
c = 3 × 10⁸ m/s
∴ < u > = 1400 W/m² / 3 × 10⁸ m/s
< u > = 4.67 × 10⁻⁶ Ws/m³ (NOTE: Ws = J)
< u > = 4.67 × 10⁻⁶ J/m³
This is the average energy density
(b) From the formula
[tex]< u > = \epsilon _{o} E_{rms} ^{2}[/tex]
[tex]E_{rms} = \sqrt{\frac{< u >}{\epsilon_{o} } }[/tex]
From the question, [tex]\epsilon _{o}[/tex] = 8.854 × 10⁻¹² C²/N.m²
∴ [tex]E_{rms} = \sqrt{\frac{4.67 \times 10^{-6} }{ 8.854 \times 10^{-12} }[/tex]
[tex]E_{rms} = 726.25 V/m[/tex]
This is the rms value of the electric field
For the rms value of the magnetic field
From
[tex]\epsilon_{o} E_{rms}^{2} = \frac{B_{rms}^{2}}{\mu _{o} }[/tex]
Then,
[tex]{B_{rms} = \sqrt{\mu _{o} \epsilon_{o} E_{rms}^{2}}[/tex]
From the question, [tex]\mu_{o}[/tex] = 4π × 10⁻⁷ T.m/A
[tex]{B_{rms} = \sqrt{4\pi \times 10^{-7} \times 8.854 \times 10^{-12} \times (726.35)^{2} }[/tex]
[tex]{B_{rms} = 2.42 \times 10^{-6} T[/tex]
This is the rms value of the magnetic field
