Chapter 21
9. We assume the spheres are far apart. Then the charge distribution on each of them
is spherically symmetric and Coulombs law can be used. Let q1 and q2 be the original
charges. We choose the coordinate system so the force on q2 is positive if

Department of Civil and Environmental Engineering
Faculty of Science and Technology
University of Macau
CEEB211
Mechanics of Materials
Laboratory report No. 1
Tension Test
By
Name:
Kuong Wai San
No:
DB426481
Date:
2015/10/07
7
Abstract
The tension test is

Practice Report for Surveying (CEEB212)
Department of Civil and Environmental Engineering
Faculty of Science and Technology
University of Macau
Practice Title: Distance Measurement with Tape
Date of Practice:
Date of Submission:
31/08/2015
07/09/2015
Grou

Name:
Student ID:
Major:
Homework 4 of Matb 210 Engineering Mathematics I
Write your answer on extra sheet of paper, if necessary
Due 14/10/2015.
Implicit Function Theorem II. Let S : F (x, y, z) = k be a level surface dened by
a dierentiable scalar funct

Section 1.1
1
, then:
x
1
1
(a) f (a) =
= ;
a
a
1
(b) f (a1 ) = 1 = a;
a
1
1
(c) f ( a ) = = 1/2 = a1/2 ;
a
a
C01S01.001: If f (x) =
(d) f (a2 ) =
1
= a2 .
a2
C01S01.002: If f (x) = x2 + 5, then:
(a) f (a) = (a)2 + 5 = a2 + 5;
(b) f (a1 ) = (a1 )2 + 5 = a

Chapter 33
15. (a) The average rate of energy flow per unit area, or intensity, is related to the
2
electric field amplitude Em by I = Em / 2 0c , so
(
)(
)(
Em = 2 0 cI = 2 4 107 H/m 2.998 108 m/s 10 106 W/m 2
= 8.7 102 V/m.
(b) The amplitude of the magn

Chapter 30
21. (a) The frequency is
f=
(40 rev/s)(2 rad/rev)
=
= 40 Hz .
2
2
(b) First, we define angle relative to the plane of Fig. 30-44, such that the semicircular
wire is in the = 0 position and a quarter of a period (of revolution) later it will be

Chapter 31
7. Table 31-1 provides a comparison of energies in the two systems. From the table, we
see the following correspondences:
1
dx
dq
, m L, v =
= i,
C
dt
dt
1 2
1 2
1
q2
kx
,
mv Li 2 .
2
2C
2
2
x q, k
(a) The mass m corresponds to the inductance

Chapter 28
5. Using Eq. 28-2 and Eq. 3-30, we obtain
v
F = q(vx By v y Bx )k = q (vx (3Bx ) v y Bx )k
$
where we use the fact that By = 3Bx. Since the force (at the instant considered) is Fz k
where Fz = 6.4 1019 N, then we are led to the condition
q ( 3v

Chapter 29
5. (a) We find the field by superposing the results of two semi-infinite wires (Eq. 29-7)
r
and a semicircular arc (Eq. 29-9 with = rad). The direction of B is out of the page,
r
as can be checked by referring to Fig. 29-6(c). The magnitude of

Chapter 25
14. (a) The potential difference across C1 is V1 = 12.0 V. Thus,
q1 = C1V1 = (10.0 F)(12.0 V) = 1.20 104 C.
(b) Let C = 10.0 F. We first consider the three-capacitor combination consisting of
C2 and its two closest neighbors, each of capacitanc

Chapter 27
12. (a) For each wire, Rwire = L/A where A = r2.
Rwire =
Consequently, we have
(1.69 108 m )(0.220 m)/(0.00100 m)2 = 0.0018 .
The total resistive load on the battery is therefore
Rtot = 2Rwire + R = 2(0.0018 ) + 6.00 = 6.0036 .
Dividing this in

Chapter 26
26. The absolute values of the slopes (for the straight-line segments shown in the
graph of Fig. 26-25(b) are equal to the respective electric field magnitudes. Thus,
applying Eq. 26-5 and Eq. 26-13 to the three sections of the resistive strip,

Chapter 23
v v
16. The total electric flux through the cube is = E dA. The net flux through the
two faces parallel to the yz plane is
yz = [ Ex ( x = x2 ) Ex ( x = x1 )] dydz =
= 6
y2 =1
y1 = 0
dy
z2 = 3
z1 =1
y2 =1
y1 = 0
dy
z2 = 3
z1 =1
dz [10 + 2(4

Chapter 22
7. The x component of the electric field at the center of the square is given by
| q1 |
| q3 |
| q2 |
| q4 |
cos 45
+
2
2
2
2
(a / 2) (a / 2) (a / 2) (a / 2)
1
1
1
=
(| q1 | + | q2 | | q3 | | q4 |)
2
4p 0 a / 2
2
Ex =
1
4p 0
= 0.
Similarly,

Department of Civil and Environmental Engineering
Faculty of Science and Technology
University of Macau
Mechanic of Materials
CEEB 211
Laboratory report No.1
Tensio
n Test
By
Name: ZHANG YUNING
No: DB427391
Date: 2015/10/8
Abstract:
Its a tension test wit