If there is a field described by the vectors A→ and B→ . These are related by B→ =kA→ where k is a constant. The two vectors are found to satisfy the differential equations
1) ∇→.A→=0
2) ∇→*B→=0
questions:
1. Using these relations derive the boundary conditions that relate the values of the components of the vectors A→ and B→ 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. So please give your answer in terms of k1 and k2 .
2. Now suppose that the boundary occupies the x-y plane (z=0). In medium 1 vector A→ has components A→ = B→ =Ao(x^+z^) and k1=1. In medium 2, k2 =2. Find the components of A→ and B→f 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.