Q40
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Energy Density Of EM Waves
In a plane EM wave, the electric field oscillates sinusoidally at a frequency of 5 × 10¹⁰ ~Hz and an amplitude of 50 ~Vm⁻¹. The total average energy density of the electromagnetic field of the wave is :
[Use ε₀ = 8.85 × 10⁻¹² C² / Nm² ]
Solution
Related Formula
Utotal average = (1)/(2)ε₀ E₀²Core Logic
For an electromagnetic wave, the total average energy density is the sum of the average energy density of the electric field and the magnetic field. They are equal, so:
Uavg = UE + UB = 2UE = 2 ( (1)/(4)ε₀ E₀² ) = (1)/(2)ε₀ E₀²Where E₀ is the amplitude of the electric field.
Step 2: Substitution
Given: E₀ = 50 V/m ε₀ = 8.85 × 10⁻¹² C²/(N· m²)
Uavg = (1)/(2) × (8.85 × 10⁻¹²) × (50)² Uavg = (1)/(2) × 8.85 × 10⁻¹² × 2500 Uavg = 1.10625 × 10⁻⁸ J/m³Chapter Mix
Class 12 Physics: Electromagnetic Waves
