Question E3A04:
In what direction does an electromagnetic wave travel?  

Choices:  
A: It depends on the phase angle of the magnetic field  
B: It travels parallel to the electric and magnetic fields  
C: It depends on the phase angle of the electric field  
D: It travels at a right angle to the electric and magnetic fields    

Correct Answer is  D: It travels at a right angle to the electric and magnetic fields  

Correct answer: D — It travels at a right angle to the electric and magnetic fields

Why D is correct:
- In a radiating electromagnetic (EM) plane wave, the electric field $\vec E$, magnetic field $\vec H$, and direction of propagation form a mutually perpendicular (orthogonal) set.
- The power flow (and thus propagation direction) is given by the Poynting vector:
  $$\vec S = \vec E \times \vec H$$
  which points at a right angle to both $\vec E$ and $\vec H$.

Why the other choices are incorrect:
- A: “It depends on the phase angle of the magnetic field” — The propagation direction does not depend on phase angle. In free space, $\vec E$ and $\vec H$ are in phase and perpendicular; phase does not determine direction.
- B: “It travels parallel to the electric and magnetic fields” — False. The wave travels perpendicular to both fields, not parallel.
- C: “It depends on the phase angle of the electric field” — Same issue as A. Phase is not what sets direction; the cross product $\vec E \times \vec H$ does.

Useful formulas and rules of thumb:
- Direction of propagation (power flow): $$\vec S = \vec E \times \vec H$$
- Orthogonality in a plane wave: $$\vec k \perp \vec E \quad \text{and} \quad \vec k \perp \vec H$$ where $\vec k$ points in the direction of propagation.
- Wave impedance in free space: $$|\vec E| = \eta_0 |\vec H|,\quad \eta_0 \approx 377\ \Omega$$
- Right-hand rule: index finger along $\vec E$, middle finger along $\vec H$, thumb points in the direction the wave travels.