# ECE221H1S: ELECTRIC AND MAGNETIC FIELDS - Skule Courses

Electronics - Devices

Oct 18, 2013 (4 years and 7 months ago)

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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:
3.4 (a): ܤ

= −

= −

(b): ܤ

= 6 −2ܤ

3.9: Solution on CD
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
3.23 (c): Solution on CD
3.24 (c): Answer in Appendix D
3.25 (c): ܣ = 12
(d): Solution on CD
3.27 (a): ܵ =
ସగ

m
2
(b): ܸ =
଼గ

m
3

3.33: ۯ = −૖

at ܲቀ2,

,

3.34 (c): ۱ = 0.707ܚ

+4ܢ

at ܲ

1,−1,2

Chapter 4
4.12: Solution on CD
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 z-component
(b) The force on a test charge at (5, 0, 6) has no x-component.

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.phy-astr.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
(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
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?