Answer: ∇²E = μ_0ε_0 ∂²E/∂t² (wave equation with speed c).
- A ∇²E = μ_0ε_0 ∂²E/∂t² (wave equation with speed c)
- B ∇²E = -kE, the time-independent Helmholtz equation form
- C ∇E = μ_0ε_0 ∂E/∂t, using a first derivative instead of second derivatives
- D ∇E = 0, as if the electric field had no spatial variation at all
Correct answer: A. ∇²E = μ_0ε_0 ∂²E/∂t² (wave equation with speed c)
Explanation: Combining Maxwell's equations gives the wave equation: ∇²E = μ_0ε_0 ∂²E/∂t². Comparing with the general wave equation ∇²E = (1/v²)∂²E/∂t² gives v = 1/√(μ_0ε_0) = c.
In an electromagnetic wave, the oscillating electric field (E) and magnetic field (B) are perpendicular to each other and to the direction the wave travels - a purely transverse wave that needs no medium, unlike sound.
Concept context
Maxwell's equations, EM spectrum, properties, and applications of each band.