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Question:

If electron charge e, electron mass m, speed of light in vacuum c, and Planck's constant h are taken as fundamental quantities, the permeability of vacuum μ₀ can be expressed in units of (mc²/he²), (hme²), (hc/me²), (hce²)?

(hme²)

(hc/me²)

(hce²)

(mc²/he²)

Solution:

The fine structure constant is defined as α = e²/(4πε₀ħc) and is dimensionless where ħ = h/(2π)
∴ α = e²/(4πε₀ħc)² = e²c/(4πε₀ħc²)
where c = 1/√(ε₀μ₀)
→ μ₀ = (ħe²)/c