The far-field pattern of an antenna can be modeled as the two dimensional Fourier Transform of the aperture.

1. Determine the 2D Fourier Transform for the function

This will require two transformations from rectangular coordinates, one in the spatial domain and one in the frequency domain. There are two key transformations. Explain.

Hint: This problem involves Bessel functions of the first kind of orders zero and one.

3) The figure illustrates a split circular cylinder of radius b and infinite length with equal and opposite potentials on the surfaces.

1.      Determine V(r,Φ) inside the tube.

2.      Provide a detailed discussion supporting your analysis of the boundary conditions