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A region shown below contains a perfect conducting half-space and air. The surface current Kₛ on the surface of the perfect conductor is Kₛ = x̂ 2 amperes per meter. The tangential H field in the air just above the perfect conductor is

1. (x̂ + ẑ) 2 amperes per meter
2. x̂ 2 amperes per meter
3. −ẑ 2 amperes per meter
4. ẑ 2 amperes per meter

Correct answer: ẑ 2 amperes per meter

Solution

The correct option is ẑ 2 amperes per meter because, according to boundary conditions at the interface of a perfect conductor and air, the tangential magnetic field (H) must be perpendicular to the surface current (Kₛ). Since Kₛ is in the x-direction, the resulting H field must be in the z-direction to satisfy these conditions.

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