DO NOT BEGIN THIS EXAM UNTIL TOLD TO START
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Instructor: ________________________________________
ELEE 2317
Applied Electricity and Magnetism
Exam 1
Oct. 9, 1999
1. This exam is closed book and closed notes. No calculators or
computers of any kind are allowed.
2. Show all of your work. No credit will be given if the work required
to obtain the solutions is not shown.
3. Perform all your work on the paper provided.
4. Write neatly. You will not be given credit for work that is not easily
legible.
5. Show units in all of your final answers.
6. Circle your final answers.
7. If you have any questions, ask the instructors. You will not be
given credit for work that is based on a wrong assumption.
8. You will have a total of 90 minutes.
_____/20 Prob. 1
_____/20 Prob. 4
_____/20 Prob. 2
_____/20 Prob. 5
_____/20 Prob. 3
Total _______/100
1
ROOM FOR EXTRA WORK
2
Problem 1 (20 pts)
Eight equal point charges of 1 [C] are arranged on the corners of a cube as shown below.
Each edge of the cube has a length of 1 [m]. Find the electric field vector E at an
observation point that is located at the center of the top face of the cube (shown by a
hollow dot in the figure). Hint: you may consider symmetry as much as possible to save
yourself work. However, explain clearly what you are doing.
z
y
x
3
ROOM FOR EXTRA WORK
4
Problem 2 (20 pts)
A point charge of strength q [C] is located at the center of a spherical cloud of
nonuniform charge density ρ v = (2 − r / a ) [C/m3]. Find the vector electric field E at all
points in space, including the region inside the charge density and outside the charge
density.
z
q
a
ρv
x
5
y
ROOM FOR EXTRA WORK
6
Problem 3 (20 pts)
A line charge having a nonniform charge density ρ  = 3z [C/m] is located on the z axis
between z = -1 [m] and z = +1 [m], as shown below. Find the vector electric field E at an
observation point on the positive z axis above the line charge, at (0, 0, h). (The
observation point is shown by a hollow dot in the figure.)
z
b0,0,hg
+1[ m]
x
−1[ m]
bg
ρ z
7
y
ROOM FOR EXTRA WORK
8
Problem 4 (20 pts)
A current density
b g
J = z 3z
[A / m2 ]
exists everywhere in space. Determine the total current that crosses a spherical surface S
defined by r = 1 [m], crossing the surface in the outward direction.
z
S
J
1.0
x
9
y
ROOM FOR EXTRA WORK
10
11
Problem 5 (20 pts)
An electric field is given by
E=
( 2 x − 1) xˆ + ( x + x 2 y ) yˆ + yzˆ
[V/m].
Determine the volume charge density everywhere that produces this field.
12