Solutions HW3.pdf - CHAPTER 3 – 9th Edition 3.1. Suppose...

3.2. An electric field in free space is E = (5 z
2
/
0
) ˆ a
z
V/m. Find the total charge contained within
a cube, centered at the origin, of 4-m side length, in which all sides are parallel to coordinate
axes (and therefore each side intersects an axis at ± 2.

3.3. Consider an electric dipole in free space, consisting of a point charge q at location z = + d/ 2,
and a point charge - q at location z = - d/ 2. The electric field intensity in the xy plane is
(see Problem 2.7):
E =
- qd a
z
4 π
0
[ ρ 2 + ( d/ 2) 2 ] 3 / 2
where ρ 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’ Law: In the dipole configuration, all field
lines terminate on the two charges. Therefore, a closed surface that is drawn around the
upper charge, and which includes the entire xy plane will show outward flux that passes
through the xy plane only. This flux will equal the enclosed charge of q .