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electrostatic boundary conditions

(See attached file for full problem description with proper symbols and equations)

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If there is a field described by the vectors A and B. These are related by =k where k is a constant. The two vectors are found to satisfy the differential equations
1) =0
2) =0

questions:
1. Using these relations derive the boundary conditions that relate the values of the components of the vectors and on the two sides of a boundary between materials 1 and 2, where the constant k has two different values k and k in materials 1 and 2 respectively. So please give your answer in terms of k and k .
2. Now suppose that the boundary occupies the x-y plane (z=0). In medium 1 vector has components and =1. In medium 2, =2. Find the components of and in medium 2.

Please explain the steps as you go. I want to be able to understand how this problem was solved and what is happening.

Attachments

Solution Summary

The electrostatic boundary conditions on the two sides of a boundary between materials 1 and 2, where the constant k has two different values k1 and k2 in materials 1 and 2 respectively is calculated in terms of k1 and k2 . and teh components of the vectors in both media were calculated. .
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