In a plane EM wave, the electric field oscillates sinusoidally at a frequency of 5 × 10¹⁰ ~Hz$5 \times 10^{10} \mathrm{~Hz}$ and an amplitude of 50 ~Vm⁻¹$50 \mathrm{~Vm}^{-1}$. The total average energy density of the electromagnetic field of the wave is : [Use ε₀ = 8.85 × 10⁻¹² C² / Nm²$\varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 / \text{Nm}^2$ ]

Related Formula

Core 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:

Where E₀$E_0$ is the amplitude of the electric field.

Step 2: Substitution

Given: E₀ = 50 V/m$E_0 = 50 \mathrm{\, V/m}$ ε₀ = 8.85 × 10⁻¹² C²/(N· m²)$\epsilon_0 = 8.85 \times 10^{-12} \mathrm{\, C^2/(N\cdot m^2)}$

Chapter Mix

Class 12 Physics: Electromagnetic Waves