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Using Divergence (Gauss) and Curl (Stokes) Theorems

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

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1. In the year 2075 physicists discover a new field described by the vectors and . These are related by

= k

Where k is constant. The two vectors are found to satisfy the differential equations

* = 0

(* means dot)

And

x = 0

a. 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 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 has components = = F0 ( ) and k1 = 1. In medium 2, k2=2. Find the components of and in medium 2.

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The point of this assignment is that you reproduce the application of the Divergence (Gauss) and Curl (Stokes) theorems in a way similar to what you have been shown in your textbook and/or in ...

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