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Asked in GSEB Board March 2020 (old course) · Impedance, dimensions and radar
Idea: the one relation that ties μ₀ and ε₀ to something familiar is c = 1/(√μ₀ε₀).
Squaring and rearranging gives μ₀ε₀ = 1/(c²).
So the unit of μ₀ε₀ is the unit of 1/(c²), that is (m s⁻¹)⁻², which is written (s m⁻¹)².
As a number, μ₀ε₀ = 1/((3×10⁸)²) = 1.11×10⁻¹⁷ in those units.
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