ECE 329

Homework 2

1. Gauss's law for displacement D states that f D-dS = Jy pdV over any closed surface S enclosing

a volume V in which electric charge density is specified by p(x, y, z) C/m³.

a) Applying dimensional analysis to Gauss' law fs D-dS = Sy pdV show that displacement D is

measured in units of C/m² - carefully describe your reasoning in reaching this conclusion.

b) What is the displacement flur fg DdS over the surface of a cube of volume V = L³ centered

about the origin, if p(x, y, z) = 3 C/m³ within V and L = 1 m?

c) Repeat (b) for p(x, y, z) = x² + y² + 2² C/m³. Hint: you need to compute a 3D integral of

x² + y² + 2² (using dadydz) over the box V.

d) What is the displacement flux in part (c) for any one of the square surfaces of volume V? Hint:

take advantage of the symmetry inherent in this problem.