The rms value of the electric field in an electromagnetic wave is E_rms = 200 V/m.The intensity of this wave is approximately A)53.1 W/m² B)106 W/m² C)1.59 $\times$ 10¹⁰ W/m² D)3.18 $\times$ 10¹⁰ W/m² E)1.70 kW/m²

Question

Quizplus · Accepted Answer

The intensity $I$ of an electromagnetic wave is given by the formula $I = \frac{1}{2} \epsilon_0 c E^2$, where $\epsilon_0$ is the permittivity of free space ($8.85 \times 10^{-12} \, \text{F/m}$), $c$ is the speed of light ($3 \times 10^8 \, \text{m/s}$), and $E$ is the rms value of the electric field. Given $E = 200 \, \text{V/m}$, substituting the values gives:$$I = \frac{1}{2} \times 8.85 \times 10^{-12} \, \text{F/m} \times 3 \times 10^8 \, \text{m/s} \times (200)^2 \, \text{V}^2/\text{m}^2$$$$I \approx 53.1 \, \text{W/m}^2$$This calculation shows that the intensity of the electromagnetic wave is approximately 53.1 W/m^2.

The Rms Value of the Electric Field in an Electromagnetic ×\times×

The Rms Value of the Electric Field in an Electromagnetic $\times$