Practice question
Question
The speed of electromagnetic waves in vacuum is given by \( c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}
\). If \( \mu_0 = 4 \pi \times 10^{-7} \, \text{H/m} \) and \( \varepsilon_0 = 8.85 \times 10^{-12} \,
\text{F/m} \), what is the approximate value of \( c \)?
Explanation
**Aerials produce radio waves** by rapid acceleration/deceleration of electrons in antenna driven by AC, frequency equals driving frequency, for 60 MHz, λ=c/f=3×10⁸/60×10⁶=5 m, half-wave antenna length λ/2=2.5 m, efficient radiation when antenna size comparable to λ. c = (1/√(μ₀ ε₀)) . Substituting values, μ₀ ε₀ = (4 π × 10⁻⁷) × (8.85 × 10⁻¹²) ≈ 1.11 × 10⁻¹⁷ . Thus, c = (1/√(1.11 × 10⁻¹⁷)) ≈ 3 × 10⁸ m/s . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 3 × 10⁸ m/s, illustrating EM wave transverse nature and Maxwell's displacement current concept.
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