Question E3A14:
What are circularly polarized electromagnetic waves?  

Choices:  
A: Waves with an electric field bent into a circular shape  
B: Waves with rotating electric and magnetic fields  
C: Waves that circle Earth  
D: Waves produced by a loop antenna    

Correct Answer is  B: Waves with rotating electric and magnetic fields  

To understand circular polarization, think about what the fields do at a fixed point in space as time passes.

Why the correct answer is correct (B)
- In a circularly polarized wave, the electric field vector rotates with constant magnitude, tracing a circle in the plane perpendicular to the direction of propagation. The magnetic field also rotates, remaining orthogonal to the electric field and to the direction of travel. That is exactly “waves with rotating electric and magnetic fields.”

Why the other choices are incorrect
- A: “Electric field bent into a circular shape” suggests a spatial curve in space at one instant, which is not what polarization describes. Polarization describes the time evolution of the field vector’s direction at a point.
- C: “Waves that circle Earth” refers to propagation paths (e.g., great-circle paths), not polarization.
- D: “Produced by a loop antenna” is not inherently true. A simple loop typically produces linear polarization in the far field. Circular polarization requires two orthogonal components in time quadrature (e.g., crossed dipoles with 90° phase shift, or an axial-mode helix), not just any loop.

Useful formulas and rules of thumb
- Condition for circular polarization from orthogonal components:
  $$|E_x| = |E_y|,\quad \Delta\phi = \pm 90^\circ$$
  Example representation:
  $$E_x = E_0 \cos(\omega t - kz),\quad E_y = E_0 \sin(\omega t - kz)$$
  The sign of the phase leads or lags sets right-hand vs left-hand circular polarization.
- Polarization mismatch loss:
  - Linear vs linear with angle $\theta$: loss factor $=\cos^2\theta$.
  - Linear antenna receiving circular wave: −3 dB (half the power).
  - Opposite-sense circular (RHCP vs LHCP): ideally infinite rejection (very large loss).