Chapter 3, Problem 3.3P

Consider an electric dipole in free space, consisting of point charge q at location 2 = +d'2, and point charge -q at location z = -d/2. The electric field intensity in the xy plane is (see Problem 2.7):

$E=\frac{da:}{4r_0|p^2+{\left(d/2\right)}^2|2/2}$

where p is the radius from the origin in cylindrical coordinates.

(a) Determine the net electric flux associated with this field that penetrates the xy plane. (b) Interpret your result as it relates to Gauss’s law.