GRADUATE PROGRAM IN ELECTRICAL ENGINEERING – UFPE

PGEE936 – ADVANCED ELECTROMAGNETICS 2021.01

Instructor: Eduardo Fontana

HOMEWORK # 4 – 05/19/2021

COMPLETION DEADLINE – 06/09/2021

Remarks:

· Homework must be handwritten, and solved clearly and concisely.

· Clear reasoning should be demonstrated in the solution development

1. Consider a dielectric cylinder, infinitely long, with the z axis as the axis of symmetry. The cylinder has radius a and electric permittivity ε. Region r > a is vacuum. The cylinder is immersed in a field region that was uniform in the absence of the cylinder and orthogonal to its axis of symmetry. Define your own coordinate system and determine:

a) The potential inside and outside the cylinder.

b) The electric field vector inside and outside the cylinder.

2. Solve the following problems from Chapter 4 of ref.[2]: 4.8 and 4.10

3. Solve the following problems in Chapter 4 of ref. [3]: 4.1, 4.3, 4.6, 4.7, 4.8

4. A thin plate of resistive material having a square shape, with each side measuring h has two edges subjected to a potential difference. For all purposes, consider that the field inside the plate that produces the current flow between electrodes is uniform, thus producing a surface current density that is also uniform, given by where t is the thickness of the plate and is the current density. A circular perforation of radius a is then made in the center of the plate, with a << h. Define your own coordinate system and determine the current distribution on the perforated plate.

5. In a solid conductor, current flows with constant current density. Assume that a spherical cavity is made in this conductor with radius a with a much smaller than the smallest linear dimension of the conductor. That is, for all intents and purposes the conductor can be considered infinite in extension. Define your own coordinate system and determine the current density around the spherical cavity.

6. Solve the following problems in Chapter 5 of ref.[3]: 5.1, 5.2, 5.3, 5.4, 5.5, 5.7, 5.8

References:

[1] Fontana, "Advanced Electromagnetics", Lecture notes #13 to #16

[2] D. Jackson, "Classical Electrodynamics".

[3] Fontana, "Eletromagnetismo - Parte 1", e-book.