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Question

An electromagnetic wave in vacuum has a magnetic field amplitude of \( B_0 = 2 \times 10^{-8} \,
\text{T} \). What is the electric field amplitude? (Given \( c = 3 \times 10^8 \, \text{m/s} \))

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Explanation

**Energy in EM wave** equally divided between electric and magnetic fields, energy density u = ½ ε₀ E² + B²/(2μ₀) = ε₀ E² = B²/μ₀, average u_avg = ½ ε₀ E₀², intensity I = c u_avg = ½ c ε₀ E₀² = E₀ B₀/(2μ₀) = c B₀²/(2μ₀), radiation pressure p = I/c for absorption, 2I/c for reflection. Using E₀ = B₀ c , we have E₀ = (2 × 10⁻⁸) × (3 × 10⁸) = 6 V/m . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 6 V/m, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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