In a plane electromagnetic wave traveling in the +x direction in vacuum, which of the following correctly describes the orientation of E and B?
AE and B are parallel to each other, both perpendicular to x
BE and B are perpendicular to each other and both perpendicular to x
CE points along x; B is perpendicular to x
DE and B are perpendicular to each other but oscillate 90° out of phase in time
EM waves are transverse: both E and B lie in the plane perpendicular to the propagation direction. They are also perpendicular to each other (their cross product E×B must point along +x, the direction of energy flow). Critically, they oscillate exactly in phase in time — both reach their maxima simultaneously. The 90° out-of-phase option confuses traveling EM waves with inductor behavior in AC circuits.
Question 2 True / False
In a traveling electromagnetic wave, the electric and magnetic fields are 90° out of phase with each other in time, similar to how voltage and current behave in an AC inductor.
TTrue
FFalse
Answer: False
In a traveling EM wave, E and B are exactly in phase — they reach their maxima, minima, and zero crossings at the same instant and location. The 90° phase relationship applies to inductors in circuits, not to propagating waves. In a standing wave (superposition of two opposing traveling waves), E and B are 90° out of phase in time, which may be the source of this confusion.
Question 3 Short Answer
The speed of light is c = 1/√(μ₀ε₀). Explain conceptually why the electric and magnetic constants of free space determine the propagation speed.
Think about your answer, then reveal below.
Model answer: Maxwell's equations couple a changing E field to a B field and vice versa. ε₀ and μ₀ set the strength of these couplings. The wave speed is determined by how quickly each field can drive the other, which is set by these two constants.
ε₀ (permittivity) governs how strongly an electric field responds to its sources; μ₀ (permeability) governs how strongly a magnetic field responds to current. When the curl equations are combined to derive the wave equation, these constants appear together: ∂²E/∂t² = (1/μ₀ε₀)∂²E/∂x². The coefficient 1/μ₀ε₀ is the square of the wave speed, just as in any wave equation of the form ∂²u/∂t² = v²∂²u/∂x². Plugging in the measured values gives c ≈ 3×10⁸ m/s — matching the measured speed of light.