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The electric field of an electromagnetic wave is E = 20 sin(w*(t - x/c)) j V/m, where w is the angular frequency and c is the speed of light. Calculate the total electromagnetic energy stored in a volume of 5 * 10^(-4) m³. (Given: epsilon₀ = 8.85 * 10^(-12) C²/(N*m²))

1. 28.5 * 10^(-13) J
2. 17.7 * 10^(-13) J
3. 8.85 * 10^(-13) J
4. 88.5 * 10^(-13) J

Correct answer: 88.5 * 10^(-13) J

Solution

The average energy density is u = epsilon₀ * E0² / 2. With E0 = 20 V/m and V = 5 * 10^(-4) m³, U = epsilon₀ * E0² / 2 * V = 8.85 * 10^(-12) * 400 / 2 * 5 * 10^(-4) = 88.5 * 10^(-13) J.

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