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(See attached file for full problem description)

Finding E for a dipole moment at origin

The problem is included in the attached Word file. An electric dipole of moment p is located at the origin. The dipole creates an electric potential at r given by Find the electric field E

Scalar and vector potentials

(See attached file for full problem description)

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Please show all steps using smith chart. (See attached file for full problem description)

An infinite cylinder of radius "a" with dielectric constant

An infinite, cylinder of radius a with dielectric constant k=(e/eo) has it axis along the z-axis. There is a uniform electric field E=Eox a large distance from the cylinder. What is the electric field everywhere inside and outside the cylinder? What is the bound charge density on the surface of the cylinder? How the field diagram showing the electric field everywhere would look like? Please look at the attached file since it contains the right vector notation. Thank you so much.