How much energy is transported across a 1.00-cm² area per hour by a sinusoidal electromagnetic wave whose $\vec { E }$ field has the amplitude of 30.4 V/m? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²,μ₀ = 4π × 10^-7 T ∙ m/A,c = 3.0 × 10⁸ m/s) A)0.44 nJ B)0.44 μJ C)0.44 mJ D)0.44 J

Question

Quizplus · Accepted Answer

The energy transported by an electromagnetic wave per unit area per unit time is given by the Poynting vector's magnitude, $S = \frac{1}{2} \sqrt{\frac{\epsilon_0}{\mu_0}} E^2$. Substituting the given values, $E = 30.4 \, \text{V/m}$, $\epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2/\text{N} \cdot \text{m}^2$, and $\mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}$, we find $S$ and then multiply by the area (1.00 cm^2 = 1.00 × 10^{-4} m^2) and the time (1 hour = 3600 seconds) to get the energy in joules. The calculation yields a value in the order of joules, making option D correct.

How Much Energy Is Transported Across a 1 E⃗\vec { E }E

How Much Energy Is Transported Across a 1 $\vec { E }$