Rms Fields And Intensity

Extending NCERT Class 12, Chapter 8 (Electromagnetic Waves), the average intensity of a plane electromagnetic wave is I = ½ ε₀ c E₀², where the factor of one half comes from time-averaging the squared sinusoidal field over a cycle, since the average of sin² over a full period is exactly one half. The intensity represents the mean power carried per unit area by the combined electric and magnetic fields, and it can equally be written as the product of the average total energy density and the speed of light. Substituting ε₀ = 8.85 × 10⁻¹² C²/N·m², c = 3 × 10⁸ m/s, and E₀ = 30 V/m gives I = ½ × 8.85 × 10⁻¹² × 3 × 10⁸ × 900 = 1.19 W/m². The value 2.39 W/m² is double the correct result because it omits the one-half averaging factor. The value 0.60 W/m² is roughly half of the true value, arising from an extra erroneous factor of one half. The value 4.78 W/m² overcounts by a factor of four, likely from mishandling both the averaging factor and the square of the field. A magnitude check confirms that a modest 30 V/m field yields an intensity of about one watt per square metre, consistent with the correct answer.