Intensity And Poynting Vector

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A laser delivers an average intensity of 6.0 W/m² onto a screen, and a researcher needs the average energy density of the beam in that region.

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Building on NCERT Class 12, Chapter 8 (Electromagnetic Waves), the intensity of an electromagnetic wave equals the average energy flowing per unit area per unit time and is related to the average energy density u by I = u·c, because the energy contained in the fields is transported forward at the speed of light. One can picture a column of the wave of cross-section one square metre: in one second it advances a distance c, so all the energy stored in that length of column, namely u·c, crosses the unit area, which is exactly the intensity. Rearranging gives u = I/c = 6.0 / (3 × 10⁸) = 2.0 × 10⁻⁸ J/m³. This small value reflects how thinly energy is spread through the volume even for a visible beam. The value 1.8 × 10⁹ J/m³ is wrong because it multiplies intensity by c rather than dividing, giving an impossibly large density. The value 5.0 × 10⁻⁷ J/m³ uses an incorrect numerical factor unrelated to I/c. The value 3.0 × 10⁻⁹ J/m³ arises from a power-of-ten error while dividing by the speed of light. A dimensional and magnitude check confirms that dividing W/m² by m/s gives J/m³ and yields a plausibly tiny density, validating the correct answer.

Intensity And Poynting Vector

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