How much energy is transported across a 1.00-cm² area per hour by a sinusoidal electromagnetic wave whose electric field has a maximum strength 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

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Quizplus · Accepted Answer

The energy transported by an electromagnetic wave per unit area per unit time (the intensity, I) can be calculated using the formula $I = \frac{1}{2} \epsilon_0 c E_0^2$, where $\epsilon_0$ is the permittivity of free space, $c$ is the speed of light, and $E_0$ is the maximum electric field strength. Plugging in the given values, $I = \frac{1}{2} (8.85 \times 10^{-12} \, \text{C}^2/\text{N} \cdot \text{m}^2) (3.0 \times 10^8 \, \text{m/s}) (30.4 \, \text{V/m})^2$, gives the intensity. To find the total energy transported across a 1.00-cm^2 area in one hour, multiply the intensity by the area and the number of seconds in an hour (3600 s). The calculation yields a value in joules, indicating that the correct answer is in the order of joules, not nanojoules, microjoules, or millijoules.

How Much Energy Is Transported Across a 1