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

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

Correct answer: 35.2 x 10⁻¹² J/m³

Solution

The average energy density of the electric field in an EM wave is u_E = (1/2)*epsilon₀*E_rms² = (1/2)*epsilon₀*(E0²/2) = epsilon₀*E0²/4. Substituting: (8.8e-12 * 16)/4 = 35.2e-12 J/m³.

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