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Question

An electromagnetic wave in vacuum has a magnetic field amplitude of \( B_0 = 4 \times 10^{-8} \,
\text{T} \). What is the electric field amplitude? (Given \( c = 3 \times 10^8 \, \text{m/s} \))

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Explanation

**EM wave in vacuum** transverse, E and B perpendicular to propagation and to each other, E×B along propagation, in phase, E/B = c =3×10⁸ m/s, c =1/√(μ₀ ε₀), μ₀=4π×10⁻⁷ H/m, ε₀=8.85×10⁻¹² F/m. For E₀=45 V/m, B₀=E₀/c=45/3×10⁸=1.5×10⁻⁷ T=150 nT, illustrating B much smaller than E. Using E₀ = B₀ c , we have E₀ = (4 × 10⁻⁸) × (3 × 10⁸) = 12 V/m . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 12 V/m, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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