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nitude of the gravitational force mg is on the order of 10 for an electron and on the order of 10 for a proton.
Chapter 23
Electric Fields
Summary
Definitions
S
S
The electric field E at some point in space is defined as the electric force F e that acts on a small positive test
charge placed at that point divided by the magnitude q 0 of the test charge:
S
E ;
S
Fe
q0
(23.7)
Concepts and Principles
Electric charges have the following important properties:
Conductors are materials in which
electrons move freely. Insulators are
materials in which electrons do not
move freely.
r Charges of opposite sign attract one another, and charges of the
same sign repel one another.
r
system is conserved.
714 The total charge
Chapterin23an isolated
Electric Fields
r Charge is quantized.
Coulomb’s law states that the electric force exerted by a
point charge q 1 on a second point charge q 2 is
S
F 12 5 k e
q 1q 2
r
2
The electric field due to a group of point
charges can be obtained by using the superposition principle. That is, the total electric
field at some point equals the vector sum of
the electric fields of all the charges:
E 5 ke a
i
qi
ri 2
r^ i
S
(23.6)
r^ 12
where r is the distance between the two charges and r^ 12 is
a unit vector directed from q 1 toward q 2. The constant ke ,
which is called the Coulomb constant, has the value ke 5
8.988 3 109 N ? m2/C2.
S
continued
At a distance r from a point charge q, the electric field due to the charge is
E 5 ke
q
r2
(23.9)
r^
where r^ is a unit vector directed from the charge
toward the point in question. The electric field is
directed radially outward from a positive charge
and radially inward toward a negative charge.
The electric field at some point due to a continuous charge
distribution is
E 5 ke 3
S
dq
r2
(23.11)
r^
where dq is the charge on one element of the charge distribution
and r is the distance from the element to the point in question.
(23.10)
Analysis Models for Problem Solving
Particle in a Field (Electric) A source particle with some electric charge establishes an electric
S
field E throughout space. When a particle with charge q is placed in that field, it experiences an
electric force given by
S
S
(23.8)
Fe 5 q E
Objective Questions
S
E
q
S
S
Fe ! qE
1. denotes answer available in Student Solutions Manual/Study Guide
1. A free electron and a free proton are released in identical electric fields. (i) How do the magnitudes of the
electric force exerted on the two particles compare?
(a) It is millions of times greater for the electron. (b) It
is thousands of times greater for the electron. (c) They
are equal. (d) It is thousands of times smaller for the
electron. (e) It is millions of times smaller for the electron. (ii) Compare the magnitudes of their accelera-
The field lines are parallel to the electron’s velocity
and pointing in the same direction as the velocity. How
far does the electron travel before it is brought to rest?
(a) 2.56 cm (b) 5.12 cm (c) 11.2 cm (d) 3.34 m (e) 4.24 m
5. A point charge of 24.00 nC is located at (0, 1.00) m.
What is the x component of the electric field due to
the point charge at (4.00, 22.00) m? (a) 1.15 N/C