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An electromagnetic wave of frequency 1 x 10¹⁴ Hz propagates along the z-axis with an electric field amplitude of 4 V/m. Given epsilon₀ = 8.8 x 10⁻¹² C²/(N*m²), what is the average energy density of the electric field?

1. 35.2 × 10⁻¹⁰ J/m³
2. 35.2 × 10⁻¹¹ J/m³
3. 35.2 × 10⁻¹² J/m³
4. 35.2 × 10⁻¹³ J/m³

Correct answer: 35.2 × 10⁻¹² J/m³

Solution

For a sinusoidal EM wave, the time-averaged electric energy density is u_E = (1/4)*epsilon₀*E0² = (1/4) * 8.8e-12 * 16 = 35.2e-12 J/m³.

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