Poynting vector: The magnitude of the Poynting vector of a planar electromagnetic wave has an average value of 0.939 W/m². The wave is incident upon a rectangular area, 1.5 m by 2.0 m, at right angles. How much total electromagnetic energy falls on the area during 1.0 minute? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²) A) 170 J B) 210 J C) 250 J D) 300 J E) 340 J

Question

Quizplus · Accepted Answer

The average power of the wave is given by:$$P_{avg} = \frac{1}{2}c\epsilon_0 E_0^2$$where c is the speed of light, $\epsilon_0$ is the permittivity of free space, and $E_0$ is the amplitude of the electric field.The total energy falling on the area during 1.0 minute is given by:$$E = P_{avg}At$$where A is the area of the rectangle and t is the time.Substituting the given values, we get:$$E = \frac{1}{2}(3.0 	imes 10^8 	ext{ m/s})(8.85 	imes 10^{-12} 	ext{ C}^2/	ext{N} \cdot 	ext{m}^2)(0.939 	ext{ W/m}^2)(1.5 	ext{ m})(2.0 	ext{ m})(60 	ext{ s})$$$$E = 170 	ext{ J}$$Therefore, the correct answer is A.

Poynting Vector: the Magnitude of the Poynting Vector of a Planar