Fields at a Perfect Conductor Boundary (Normal Incidence) A TEM plane wave is normally incident on a perfect electric conductor (PEC). At the PEC surface, what are the relative magnitudes of the electric field (E) and magnetic field (H)?

Introduction / Context:
Boundary conditions at perfect conductors are a cornerstone of electromagnetic theory. They determine reflection behavior and field distributions in waveguides, cavities, and scattering problems.

Given Data / Assumptions:

• Plane TEM wave at normal incidence.
• Perfect electric conductor (infinite conductivity) so tangential E at the surface must vanish.
• Time-harmonic steady state.

Concept / Approach:

At a PEC boundary, the tangential component of the electric field is zero. The incident and reflected waves superpose to enforce E_t = 0 at the surface, producing a pressure node (minimum). The magnetic field forms a standing-wave antinode (maximum) at the surface, driving surface currents necessary to cancel the tangential E.

Step-by-Step Solution:

Verification / Alternative check:

Using standing-wave relations for normal incidence, the E field has a node at the surface; the H field has an antinode at the surface, consistent with power not penetrating the PEC.

Why Other Options Are Wrong:

Options B, C, and D contradict the PEC boundary conditions; E cannot be maximum at the surface, and H need not vanish.

Common Pitfalls:

Confusing E and H boundary behavior; assuming both go to zero at metal surfaces, which is false for H except in special cases inside the conductor with nonzero loss.

Final Answer:

minimum and maximum