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 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

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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