The region shown contains a perfectly conducting half-space and air. Surface current is K s=2 x A/m. Find tangential H in air just above the conductor.

GATE 2014 EC (EC3) – Question 64

Electromagnetics · Maxwell's Equations · 2 marks · Multiple choice

The region shown contains a perfectly conducting half-space and air. Surface current is $\mathbf K_s=2\hat x$ A/m. Find tangential H in air just above the conductor.

Diagram for GATE 2014 EC (EC3) question 64

$2(\hat x+\hat z)$ A/m
$2\hat x$ A/m
$-2\hat z$ A/m
$2\hat z$ A/m

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Correct answer: (D) $2\hat z$ A/m

Explanation

The outward normal from conductor to air is ŷ. The magnetic boundary condition is n̂×Hair=Ks because the ideal conductor interior field is zero. Since ŷ×ẑ=x̂ and Ks=2x̂A/m, the required tangential field is **H=2ẑA/m,D**. The sign follows the chosen outward normal.