GATE EC 2014 Set 3 — Question 64
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Electromagnetics → Maxwell's Equations → Boundary Conditions
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Question
A region shown below contains a perfect conducting half-space and air. The surface current on the surface of the perfect conductor is amperes per meter. The tangential field in the air just above the perfect conductor is 

Correct answer
(D) z2 amperes per meter
Solution
The boundary condition for the magnetic field at the surface of a perfect conductor is given by:
where is the unit normal vector pointing from the conductor into the air. From the figure, the interface is at , so .
Given .
Let . The tangential components are and .
Comparing components:
and .
Thus, the tangential field is amperes per meter.
where is the unit normal vector pointing from the conductor into the air. From the figure, the interface is at , so .
Given .
Let . The tangential components are and .
Comparing components:
and .
Thus, the tangential field is amperes per meter.
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