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Question

According to Maxwell's equations, what does the equation \( \oint \mathbf{B} \cdot \mathrm{d}
\mathbf{A} = 0 \) imply?

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Explanation

**Ampere-Maxwell law** ∮ B·dl = μ₀(I_c + ε₀ dΦ_E/dt) generalizes Ampere's law, displacement current arises from time-varying electric field, source of magnetic field like conduction current. For rate of change of flux 2×10¹¹ V·m/s, I_d = ε₀×2×10¹¹ =8.85×10⁻¹²×2×10¹¹=1.77 A. This is Gauss's Law for magnetism, which implies that there are no magnetic monopoles, as the net magnetic flux through a closed surface is zero. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields No magnetic monopoles exist, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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