The Electric Field
Study Guide for Chapter 23
Outline
1. The Electric Field of Point Charge
The electric field is a vector field associated with a charge distribution. By “vector field”, we
mean that the electric field consists of one vector E for each point in space.
The electric field at a point measures the force per unit charge that would be exerted on a
positive “test charge” placed at the point:
Eœ
F
;
The electric field is measured in newtons per coulomb (NÎC).
When a charge ; is placed in an electric field, the force on the charge is given by the formula
F œ ;E
Note that a positive charge experiences a force in the same direction as E, while a negative
charge experiences a force in the opposite direction.
A point charge U emanates an electric field in the space around it, with magnitude
determined by Coulomb's law:
Iœ
" U
%1%! <#
The electric field points away from positive charges, and towards negative charges.
If multiple charges are present, the resulting electric field is obtained by adding the electric
field vectors from the individual charges:
E œ E"  E#  E$  â
Problems: 1, 11, 13, 17, 19
2. The Electric Field of Continuous Charge Distributions
For a continuous charge distribution, each infinitesimal portion of charge .; exerts an
infinitesimal electric field .E according to Coulomb's law. To find the total electric field, all of
these infinitesimal contributions must be added together using an integral.
Though you need to understand this idea, and you should read the derivations in the section,
you will not be required to integrate over charge distributions on your own. However, you do
need to be comfortable with the formulas for the electric field derived in examples 6 and 8:
1. For an infinite line of charge,
Iœ
" #1%! <
(line of charge)
where < is the distance to the line, and - is the amount of charge per unit length.
2. For an infinite plane of charge,
Iœ
5
#% !
(plane of charge)
where 5 is the amount of charge per unit area. Note that the electric field for an infinite
plane does not depend on <.
Problems: 27, 31, 35, 37
3. Lines of Electric Field
The electric field may be represented by drawing electric field lines. The lines point in the
direction of E, and the strength of the field is proportional to the density of the field lines.
This gives a visual interpretation of the "Î<# in Coulomb's law.
4. Motion in a Uniform Electric Field
An electric field is uniform if it does not vary from place to place. A charged particle moving in
a uniform electric field experiences a constant force (since J œ ;I ), and therefore moves with
constant acceleration (since J œ 7+).
Problems: 58
(Answer: #Þ! ns; "Þ! ‚ "!' mÎs)
5. Electric Dipole in an Electric Field
You will not be responsible for the material in this section.
Answers
1. I œ &Þ% ‚ "!"% N; + œ 'Þ! ‚ "!"' mÎs#
11. I œ &Þ" ‚ "!"" NÎC
13. I œ &Þ" ‚ "!"# NÎC
#
N † m# U
U
"! N † m
17. EE œ Š"Þ"& ‚ "!
‹ # i, EF œ Š"Þ"& ‚ "!
‹ # j,
#
#
C
P
C
P
#
#
N†m U
U
"! N † m
EG œ Š"Þ"& ‚ "!"!
i
,
E
œ

"Þ"&
‚
"!
‹
Š
‹ #j
H
#
#
#
C
P
C
P
"!
19. IT œ a*Þ& ‚ "!$ i  #Þ) ‚ "!% jb NÎC
27. I!Þ& œ (Þ# ‚ "!% NÎC, I"Þ! œ $Þ' ‚ "!% NÎC, I"Þ& œ #Þ% ‚ "!% NÎC
31. E œ
" acos $!°bj
1%! #.
35. EE œ "Þ"$ ‚ "!& j NÎC,
EG œ $Þ$* ‚ "!& j NÎC,
EF œ "Þ"$ ‚ "!& j NÎC,
EH œ "Þ"$ ‚ "!& j NÎC
37. I œ #Þ% ‚ "!( NÎC at an angle of %&°
58. > œ #Þ! ns, @ œ "Þ! ‚ "!' mÎs