An electromagnetic plane wave, propagating in vacuum, has an electric field given by E = E0 cos (kx−ωt) and is normally incident on a perfect conductor at x = 0, as shown in figure. Immediately to the left of the conductor, the total electric field E and the total magnetic field B are given by which of the following?
| E | B | |
|---|---|---|
| A. | 0 | 0 |
| B. | 2E0 cos ωt | 0 |
| C. | 0 | 2(E0/c) cos ωt |
| D. | 2E0 cos ωt | 2(E0/c) cos ωt |
| E. | 2E0 cos ωt | 2(E0/c) sin ωt |
(GR0177 #61)
Solution:
Perfect conductor:
Its charge and current are distributed on the surface so that external fields can not penetrate it.
Boundary Condition (BC) on the surface of perfect conductor:
- Etangential = 0
- Enormal ≠ 0
- Btangential ≠ 0
- Bnormal = 0
EM wave: E ⊥ B (perpendicular to each other).
If E normal to the surface of conductor, B is tangential.
BC: Enormal ≠ 0
Einitial is reflected by the conductor with the same magnitude but opposite direction.
Total E = Einitial − Ereflected = 0
(B), (D), (E) FALSE
BC: Btangential ≠ 0
B is not reflected, it's parallel to the surface.
Total B ≠ 0
(A) FALSE
Answer: C
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