Problem 4.51 Figure P4.51 shows three planar dielectric slabs of equal thickness
but with diﬁerent dielectric constants. If E0 in air makes an angle of 450 with respect
to the z—axis, ﬁnd the angle of E in each of the other layers.
Figure P4.51: Dielect

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Problem 1.1
Given. : For 58:0 and t: 5075, Paul): )0 N/m"
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5.22 A long cylindrical conductor whose axis is coincident with the z—axis has a
radius a and carries a current characterized by a current density J : 210 / r, where J0
is a constant and r is the radial distance from the cylinder’s axis. Obtain an express

1. (35%) On a lossless 50- transmission line terminated with a ZL = 150+j100 . If this
transmission line is be matched to the load using a shorted load stub. Determine the
stub length and distance between the load and stub. Two possible answers. You only

Problem 4.20
Given the electric flux density
D = x 2(x + y) + y (3x 2y) (C/m2 )
determine
(a) v by applying Eq. (4.26).
(b) The total charge Q enclosed in a cube 2 m on a side, located in the first octant
with three of its sides coincident with the x-, y-

Problem
Z 3.43 For the vector fiel E =
(a)
x xy y (x2 + 2y2 ), calculate
E dl around the triangular contour shown in Fig. P3.50(a), and
n
ZC
(b)
S
E) ds over the area of the triangle.
(
Solution: In addition to the independent condition that z = 0, the t

Problem 3.33 The gradient of a scalar function T is given by
T = z e3z .
If T = 10 at z = 0, find T (z).
Solution:
T = z e3z .
By choosing P1 at z = 0 and P2 at any point z, (3.76) becomes
T (z) T (0) =
Z z
0
Z z
z e3z (x dx + y dy + z dz )
0
z
Z z
e3z

Problem 2.17
At an operating frequency of 300 MHz, a lossless 50- air-spaced
transmission line 2.5 m in length is terminated with an impedance ZL = (40 + j20) .
Find the input impedance.
Solution: Given a lossless transmission line, Z0 = 50 , f = 300 MHz,

1. (35%) A wave with the frequency of 1-MHz travels in the -z direction in air. Assume
the wave travels at the speed of light (c = 3.0x108m/s in air). If the wave reaches a peak
value of 1.2 at z =50 m when t=0. Find:
1) Wavelength in air
2) Expression fo

Problem 3.39 For the vector field E = x xz y yz2 z xy, verify the divergence
theorem by computing:
(a) the total outward flux flowing through the surface of a cube centered at the
origin and with sides equal to 2 units each and parallel to the Cartesian a