Physics 2000 @Physics2000
In the Love of Physics Solar System Joined July 2012-
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Maxwell's equations in different mathematical forms ✍️ Differential form (SI, vacuum with sources) ∇ · E = ρ / ε₀ ∇ · B = 0 ∇ × E = − ∂B/∂t ∇ × B = μ₀ J + μ₀ε₀ ∂E/∂t Integral form ∮ E · dA = Q_enc / ε₀ ∮ B · dA = 0 ∮ E · dℓ = − dΦ_B/dt ∮ B · dℓ = μ₀ I_enc + μ₀ε₀ dΦ_E/dt Covariant form ∂_μ F^μν = μ₀ J^ν ∂_[λ F_μν] = 0 The last term in the fourth equation, μ₀ε₀ ∂E/∂t, is Maxwell's own addition. Set ρ and J to zero and it gives ∇²E = μ₀ε₀ ∂²E/∂t², a wave travelling at 1/√(μ₀ε₀), which turned out to be the speed of light.
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