1. In the year 2075 physicists discover a new field described by the vectors F→ and G→ . These are related by
G→= F→
Where k is constant. The two vectors are found to satisfy the differential equations
∇→* F→ = 0
(* means dot)
And
∇→x G→= 0
a. Using these relations derive the boundary conditions that relate the values of the components of the vectors F→ and G→ 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.
b. Now suppose that the boundary occupies the x-y plane (z=0). In the medium 1 vector F→ has components F→ =G→ = F0 (x^+z^ ) and k1 = 1. In medium 2, k2=2. Find the components of F→ and G→ in medium 2.