Solving H_{s,\theta} and H_{i,\theta} Relationship on Planar Surface

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The discussion focuses on determining the relationship between the scattered magnetic field H_{s,\theta} and the incident magnetic field H_{i,\theta} on a conducting planar surface illuminated by a plane wave. The tangential boundary conditions for the electric fields E_{s} and E_{i} are established, indicating that the scattered electric field is equal in magnitude but opposite in direction to the incident electric field. Participants are urged to provide insights or equations that can clarify the relationship between the corresponding magnetic fields under these conditions. The urgency of the request highlights the need for a prompt and clear resolution to this electromagnetic problem. Understanding this relationship is crucial for applications in electromagnetic theory and engineering.
Ameilucky
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Hi,
On a conducting planar surface, with a plane wave illuminated,(s for scattered field, i for incident field) in spherical coordinates under the tangential boundary condition that:
E_{s}(\theta,\phi)=-E_{i}\theta,\phi),
which is E_{s,\phi}(\theta,\phi)=-E_{i,\phi}(\theta,\phi) and
E_{s,\theta}(\theta,\phi)=-E_{i,\theta}(\theta,\phi)
then what is the relationship between
H_{s,\theta}(\theta,\phi) and H_{i,\theta}(\theta,\phi), respectively
H_{s,\theta}(\theta,\phi)and H_{i,\theta}(\theta,\phi)?

I need to figure out this urgently, many thanks!
 
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