1
ECE221H1S:
E
LECTRIC AND
M
AGNETIC
F
IELDS
P
ROBLEM
S
ET
#1
V
ECTOR
C
ALCULUS
,
AND
C
OULOMB
’
S
L
AW
C
ALCULATIONS
F
OR
D
ISCRETE
C
HARGE
D
ISTRIBUTIONS
Workbook (Knight)
:
Chapter 26 Questions
20 – 23, 25, 26, 28, 31
Chapter 27 Questions
3, 5 – 13
Textbook (Ulaby)
:
Chapter 3:
3.1: Answer in Appendix D
3.4 (a): ܤ
௫
= −
ସ
ଷ
,ܤ
௭
= −
ଶ
ଷ
(b): ܤ
௭
= 6 −2ܤ
௫
3.7: Answer in Appendix D
3.9: Solution on CD
3.15: Answer in Appendix D
3.19: ۳
௧
= −1.5ી
+2.6
3.20 (b): Solution on CD
(d): Sketch
3.21 (b): Sketch
3.22 (b): Answer in Appendix D
(d): Answer in Appendix D
3.23 (c): Solution on CD
3.24 (c): Answer in Appendix D
3.25 (c): ܣ = 12
(d): Solution on CD
3.26: Answer in Appendix D
3.27 (a): ܵ =
ସగ
ଷ
m
2
(b): ܸ =
଼గ
ଽ
m
3
3.28: Answer in Appendix D
3.33: ۯ = −
at ܲቀ2,
గ
ଶ
,
గ
ଶ
ቁ
3.34 (c): ۱ = 0.707ܚ
ො
+4ܢ
ො
at ܲ
ଷ
ሺ
1,−1,2
ሻ
Chapter 4
4.11: Answer in Appendix D
4.12: Solution on CD
4.13: Answer in Appendix D
4.18: Solution to be discussed in tutorials
Supplemental Problems
1. Point charges Q
1
and Q
2
are, respectively, located at (4, 0, –3) and (2, 0, 1).
If Q
2
= 4 nC, find Q
1
such that
(a) The E at (5, 0, 6) has no zcomponent
(b) The force on a test charge at (5, 0, 6) has no xcomponent.
2. Charges +Q and +3Q are separated by a distances 2m. A third charge is located
such that the electrostatic system is in equilibrium. Find the location and the value of
the third charge in terms of Q.
2
Supplemental Problems (continued)
3. Consider the Hyperphysics Electricity and Magnetism Concept Map, which is
available at http://hyperphysics.phyastr.gsu.edu/hbase/emcon.html#emcon
.
Read through the following parts of this concept map and answer the associated
questions:
(a) Electric Charge
i) What is the basic unit of electric charge?
ii) What is the basic building block of a proton (i.e., what is a proton
made up of)?
(b) Coulomb’s Law and the Electric Force Example
i) What is the electrical force between a proton and an electron
separated by 0.55 angstroms (0.55 x 10
10
m, the radius of a
hydrogen atom)?
ii) Since electric forces can be quite large, then why don't we see more
dramatic displays of electrical force?
(c) Electric Field and Electric Field Electric Field of a Point Charge
i) Does the electric field of a negative point charge point towards the
charge or away from the charge?
ii) Does the electric field of a positive point charge point towards the
charge or away from the charge?
(d) Electric Field Electric Field of a Point Charge Multiple Point Charges
i) If q
1
= q
2
and r
1
= r
2
, where would the net electric field be zero?
ii) If q
1
= 2q
2
is there a location where the net electric field would be zero?
(e) Electric Field Electric Field of a Point Charge Multiple Point Charges
Calculation
i) If q
1
= q
2
= 1 mC, q
1
is located at P
1
(−1,0) m, and q
2
is located at P
2
(1,0) m
what is the net electric field at the field point P(0,0) m? Does this make
sense?
ii) If q
1
= q
2
= 1 mC, q
1
is located at P
1
(−1,0) m, and q
2
is located at P
2
(1,0) m
what is the net electric field at the field point P(0,1) m? Does this make
sense?
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