CHAPTER 11
11.1. The parameters of a certain transmission line operating at 6 108 rad/s are L = 0.4 H/m,
C = 40 pF/m, G = 80 S/m, and R = 20 /m.
a) Find , , , , and Z0 : We use
= ZY = (R + jL)(G + jC)
=
[20 + j(6 108 )(0.4 106 )][80 106 + j(6 108 )(40 10
CHAPTER 13
+ + 13.1. A uniform plane wave in air, Ex1 = Ex10 cos(1010 t z) V/m, is normally-incident on a copper surface at z = 0. What percentage of the incident power density is transmitted into the copper? We need to nd the reection coecient. The intri
CHAPTER 7 7.1. Let V = 2xy 2 z 3 and = 0 . Given point P (1, 2, 1), nd: a) V at P : Substituting the coordinates into V , nd VP = 8 V. b) E at P : We use E = V = 2y 2 z 3 ax 4xyz 3 ay 6xy 2 z 2 az , which, when evaluated at P , becomes EP = 8ax + 8ay 24az
CHAPTER 9 9.1. A point charge, Q = 0.3 C and m = 3 1016 kg, is moving through the eld E = 30 az V/m. Use Eq. (1) and Newtons laws to develop the appropriate dierential equations and solve them, subject to the initial conditions at t = 0: v = 3 105 ax m/s
CHAPTER 8 8.1a. Find H in cartesian components at P (2, 3, 4) if there is a current lament on the z axis carrying 8 mA in the az direction: Applying the Biot-Savart Law, we obtain
Ha =
IdL aR = 4R2
Idz az [2ax + 3ay + (4 z)az ] = 4(z 2 8z + 29)3/2
Idz
CHAPTER 12
12.1. Show that Exs = Aejk0 z+ is a solution to the vector Helmholtz equation, Sec. 12.1, Eq. (30), for k0 = 0 0 and any and A: We take d2 2 Aejk0 z+ = (jk0 )2 Aejk0 z+ = k0 Exs dz 2 12.2. A 100-MHz uniform plane wave propagates in a lossless m
CHAPTER 10
10.1. In Fig. 10.4, let B = 0.2 cos 120t T, and assume that the conductor joining the two ends of the resistor is perfect. It may be assumed that the magnetic eld produced by I(t) is negligible. Find: a) Vab (t): Since B is constant over the lo
CHAPTER 6. 6.1. Atomic hydrogen contains 5.5 1025 atoms/m3 at a certain temperature and pressure. When an electric eld of 4 kV/m is applied, each dipole formed by the electron and positive nucleus has an eective length of 7.1 1019 m. a) Find P: With all i
CHAPTER 4 4.1. The value of E at P ( = 2, = 40 , z = 3) is given as E = 100a 200a + 300az V/m. Determine the incremental work required to move a 20 C charge a distance of 6 m: a) in the direction of a : The incremental work is given by dW = q E dL, where
CHAPTER 5 5.1. Given the current density J = 104 [sin(2x)e2y ax + cos(2x)e2y ay ] kA/m2 : a) Find the total current crossing the plane y = 1 in the ay direction in the region 0 < x < 1, 0 < z < 2: This is found through
2 1 2 1 0
I=
S 4
J n da =
S 0 0
J ay
CHAPTER 3 3.1. An empty metal paint can is placed on a marble table, the lid is removed, and both parts are discharged (honorably) by touching them to ground. An insulating nylon thread is glued to the center of the lid, and a penny, a nickel, and a dime
CHAPTER 2 2.1. Four 10nC positive charges are located in the z = 0 plane at the corners of a square 8cm on a side. A fth 10nC positive charge is located at a point 8cm distant from the other charges. Calculate the magnitude of the total force on this fth
CHAPTER 1 1.1. Given the vectors M = 10ax + 4ay 8az and N = 8ax + 7ay 2az , nd: a) a unit vector in the direction of M + 2N. M + 2N = 10ax 4ay + 8az + 16ax + 14ay 4az = (26, 10, 4) Thus a= b) the magnitude of 5ax + N 3M: (5, 0, 0) + (8, 7, 2) (30, 12, 24)