Question

Which of the following is the primary condition that must be satisfied at the boundary of a perfect electric conductor (PEC) for an electromagnetic wave?

• A. The tangential component of the magnetic field is zero
• B. The tangential component of the electric field is zero
• C. The normal component of the electric field is zero
• D. The normal component of the magnetic field is continuous and non-zero

Hint:

Think of it this way to easily remember: electric fields terminate perpendicular to a conductor wall. They cannot run parallel along the metal surface, because if they did, the electrons would simply move to cancel them out instantly. Hence, Tangential $\mathbf{E} = 0$.

Answer 1

The Correct Option is B

Understanding the Concept: Inside an ideal, perfect electric conductor (PEC), the internal electrical conductivity approaches infinity ($\sigma \rightarrow \infty$). Because the material is an ideal conductor, any static or dynamic interior electric field would induce an infinite current flow, which is physically impossible. Therefore, the total electric field inside the body of a PEC is always zero: $$\mathbf{E}_{\text{inside}} = 0$$ Using Maxwell’s boundary conditions across two media interfaces: $$E_{t1} - E_{t2} = 0 \quad \Rightarrow \quad E_{t1} = E_{t2}$$ Where $E_{t1}$ and $E_{t2}$ represent the respective parallel/tangential electric field vector components acting directly along the interface plane boundary. Step-by-step Implementation:
• Let Medium 2 be the interior region of the Perfect Electric Conductor material, meaning $E_{t2} = 0$.
• Substituting this internal value into our boundary continuity match relation yields: $$E_{t1} = 0$$
• This demonstrates that the tangential component of the electric field must completely vanish directly at the outer boundary surface of a PEC.