Maxwell's equations predict that the speed of EM waves in vacuum equals 1/√μ₀ε₀.

Solution

Physics sir · 4 steps

Maxwell's equations give a wave equation for E and B, and its speed comes from just two constants.

1. Combine the laws. In vacuum, Faraday's law says a changing B makes E. The Ampere-Maxwell law says a changing E makes B. Combining the two gives a wave equation for each field.

   (∂² E)/(∂ x²) = μ₀ε₀ (∂² E)/(∂ t²)

2. Read off speed. A standard wave equation has the form (∂² y)/(∂ x²) = 1/v²(∂² y)/(∂ t²). Comparing the two gives 1/v² = μ₀ε₀, so v = 1/√μ₀ε₀.
3. Check the number. With μ₀ = 4π × 10⁻⁷ T m A⁻¹ and ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻², this gives v ≈ 3.0 × 10⁸ m s⁻¹. That is the measured speed of light.
4. So. The statement is true. Maxwell's equations predict EM waves in vacuum travel at c = 1/√μ₀ε₀.

The idea to keep. In vacuum c = 1/√μ₀ε₀. In a medium, replace these with μ and ε, which gives v = 1/√με = c/n.

Answer from the NTA final answer key. Solution by PrepWiser.