Reference no: EM13904981

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.