If the electric field associated with a radiation of frequency 10 MHz is E=10 sin(kx-ω t) mV m⁻¹, then its energy density is J m⁻³. (ε₀=8.85×10⁻¹² C² N⁻¹ m⁻²)

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(1) 4.425×10⁻¹⁶. Given: the amplitude is E₀=10 mV m⁻¹=10⁻² V m⁻¹, with ε₀=8.85×10⁻¹² in SI units. Idea: the wave stores energy in both fields, and over a cycle the two store equal amounts. Adding them, the average total energy density is u=1/2ε₀E₀². u=1/2×8.85×10⁻¹²×(10⁻²)²=1/2×8.85×10⁻¹⁶. u=4.425×10⁻¹⁶ J m⁻³. Notice that the frequency never enters: the energy density is set by the amplitude of the field, not by how fast it oscillates.

If the electric field associated with a radiation of frequency 10 MHz is E=10 sin(kx-ω t) mV m⁻¹, then its energy density is ______ J m⁻³. (ε₀=8.85×10⁻¹² C² N⁻¹ m⁻²)

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