ECE 329
Homework 3 Solutions
Due: Tuesday September 15, 2015, Noon
1. In electrostatics, we generate a curl-free vector eld E(x, y, z) if we take the gradient of a scalar
function V (x, y, z). Therefore, E = ( V ) = 0.
x
z
y
z
z
E =
y
x
y
x
= 0.
2. Follow
ECE 329
Homework 5 Solutions
Due: Tuesday, Sept 29, 2015, 5PM
1. To determine surface charge densities at z = 0 and z = 4 (m), we proceed as follows: Let V0 denote
the electrostatic potential at z = 2. Since (according to Laplaces equation) V (z) needs to
ECE 329
Homework 4 - Solutions
Due: Tuesday September 22, 2015, noon
1.
a) We can write E as
E=
Q
y
z
x
x 3 +y 3 +z 3 .
4 0
r
r
r
Therefore,
E =
=
Take the calculation of
y
z
r3
x
y
z
x
x
r3
Q
4 0
y
y
r3
z
z
r3
Q
z
y
x
3
4 0
y r
z r3
Q
x
z
y
3
4 0 z r
x
ECE 329
Homework 2 Solutions
Due: Tuesday September 8, 2015, 5PM
1. Gausss law for electric ux density D states that
D dS =
dV,
V
S
C
over any closed surface S enclosing a volume V where electric charge density is specied by (x, y, z) m3 .
3
Here, we wil
ECE 329
Homework 6 Solutions
Due: Tuesday, March 3, 2015, 5PM
1. The magnetic eld at the origin is a superposition of those generated by the two sheets.
a) Since the currents are owing in z direction and they extend to innity in both x and y directions,
t
ECE 329
Spring 2015
Homework 7 - Solution
Due: Tuesday Mar. 10, 2015
1. Verifying vector identity
for E = 2e
z
and H = 3e
x
y
HrE
y .
E r H = r (E H)
The left-hand side of the identity gives
x
HrE
3e
x
3e
x
ErH =
=
=
y
y
x
y
2e
z
2e
z
y
y
y
z
@
@x
3e y
3
ECE 329
Homework 1 Solutions
Due: Monday, August 31, 2015, 5PM
1. Consider the 3D vectors
A = 3 + y 2,
x
z
B = x + y z,
C = x 2 + 3,
y
z
a) The vector
D = A + B = 4 + 2 3
x
y
z
b) The vector
A + B 4C = 4 + 2 3 4( 2 + 3) = 10y 15
x
y
z
x
y
z
z
c) The ve