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In a plane EM wave, the electric field oscillates sinusoidally at a frequency of 5 × 10¹⁰ Hz and an amplitude of 50 V m⁻¹. The total average energy density of the electromagnetic field of the wave is [Use ε₀ = 8.85 × 10⁻¹² C²/Nm²]

Asked in JEE Main 31st Jan 1st Shift 2024 · Instantaneous and average energy density

• (1) 2.212 × 10⁻¹⁰ J m⁻³
• (2) 4.425 × 10⁻⁸ J m⁻³
• (3) 1.106 × 10⁻⁸ J m⁻³
• (4) 2.212 × 10⁻⁸ J m⁻³

Step-by-step solution

Why the other options are wrong

• (1) 2.212 × 10⁻¹⁰ J m⁻³ is ε₀E₀²/100 — a stray decade slipped in from the 50
• (2) 4.425 × 10⁻⁸ J m⁻³ = ε₀E₀², i.e. you used the peak density instead of the average
• (4) 2.212 × 10⁻⁸ J m⁻³ is twice the answer — you added ε₀E₀²/2 for each field instead of ε₀E₀²/4

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