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ELECTROSTATIC FORCES FORCE FIELDS
Recall that two objects with like charges, (–) and (–) or (+) Does it seem odd to you that gravitational forces and electrical
and (+), produce a repulsive force, and two objects with unlike forces can act on objects that are not touching? How can gravi-

charges, (–) and (+), produce an attractive force. The size of tational forces act through the vast empty space between Earth
either force depends on the amount of charge of each object and and the Sun? How can electrical forces act through a distance

on the distance between the objects. The relationship is known as to pull pieces of paper to your charged comb? Such questions
Coulomb’s law, which is have bothered people since the early discovery of small, light
objects being attracted to rubbed amber. There was no mental

q q
_
1 2
F = k 2 model of how such a force could act through a distance with-
d out touching. The idea of “invisible fluids” was an early attempt

equation 6.2 to develop a mental model that would help people visualize
how a force could act over a distance without physical contact.
9
2
2
where k has the value of 9.00 × 10 newton-meters /coulomb Then Newton developed the law of universal gravitation, which

9
2
2
(9.00 × 10 N·m /C ). correctly predicted the magnitude of gravitational forces acting
The force between the two charged objects is repulsive if through space. Coulomb’s law of electrical forces had similar

q 1 and q 2 are the same charge and attractive if they are diff erent success in describing and predicting electrostatic forces acting
(like charges repel, unlike charges attract). Whether the force through space. “Invisible fluids” were no longer needed to explain

is attractive or repulsive, you know that both objects feel equal what was happening, because the two laws seemed to explain the
forces, as described by Newton’s third law of motion. In addi- results of such actions. But it was still difficult to visualize what

tion, the strength of this force decreases if the distance between was happening physically when forces acted through a distance,
the objects is increased (a doubling of the distance reduces the and there were a few problems with the concept of action at a dis-
1
force to ⁄4 the original value). tance. Not all observations were explained by the model.

The work of Michael Faraday (1791–1867) and James

EXAMPLE 6.2 Maxwell (1831–1879) in the early 1800s finally provided a new
mental model for interaction at a distance. This new model

Electrons carry a negative electric charge and revolve about the nucleus
of the atom, which carries a positive electric charge from the proton. did not consider the force that one object exerts on another
The electron is held in orbit by the force of electrical attraction at a typi- one through a distance. Instead, it considered the condition of

cal distance of 1.00 × 10 –10 m. What is the force of electrical attraction space around an object. The condition of space around an elec-
between an electron and proton? tric charge is considered to be changed by the presence of the
charge. The charge produces a force fi eld in the space around

it. Since this force field is produced by an electrical charge, it is
SOLUTION called an electric fi eld. Imagine a second electric charge, called
– –19
The fundamental charge of an electron (e ) is 1.60 × 10 C, and a test charge, that is far enough away from the electric charge

+
the fundamental charge of the proton (p ) is 1.60 × 10 –19 C. Th e that forces are negligible. As you move the test charge closer
distance is given, and the force of electrical attraction can be found and closer, it will experience an increasing force as it enters the
from equation 6.2: electric fi eld. The test charge is assumed not to change the fi eld

q 1 = 1.60 × 10 –19 C that it is entering and can be used to identify the electric fi eld
q 2 = 1.60 × 10 –19 C that spreads out and around the space of an electric charge.
All electric charges are considered to be surrounded by an
d = 1.00 × 10 –10 m
electric fi eld. All masses are considered to be surrounded by a
2
9
k = 9.00 × 10 N·m /C 2
gravitational fi eld. Earth, for example, is considered to change
F = ?
the condition of space around it because of its mass. A spaceship
q q
_
1 2
F = k far, far from Earth does not experience a measurable force. But
2
d as it approaches Earth, it moves farther into Earth’s gravitational
( 9.00 × 10 _ 2 (1.60 × 10 –19 C)(1.60 × 10 –19 C) field and eventually experiences a measurable force. Likewise, a
2 )
9 N·m

_____ magnet creates a magnetic fi eld in the space around it. You can
C

=

(1.00 × 10 –10 m) 2 visualize a magnetic field by moving a magnetic compass needle
–19 ( ) (C ) around a bar magnet. Far from the bar magnet the compass nee-
_
2
N·m

2

9
–19
)(1.60 × 10
(9.00 × 10 )(1.60 × 10
2
)
____ _ dle does not respond. Moving it closer to the bar magnet, you can
C

=

1.00 × 10 –20 m 2 see where the magnetic field begins. Another way to visualize a

–28
_
2.30 × 10
__ N·m 2 C _ 2 1 _ magnetic field is to place a sheet of paper over a bar magnet, then

= × × sprinkle iron filings on the paper. Th e filings will clearly identify

2
1.00 × 10 –20 C 2 1 m
the presence of the magnetic fi eld.
–8
= 2.30 × 10 N

Another way to visualize a field is to make a map of the
The electrical force of attraction between the electron and proton is field. Consider a small positive test charge that is brought into

–8
2.30 × 10 newton. an electric fi eld. A positive test charge is always used by conven-
tion. As shown in Figure 6.6, a positive test charge is brought
144 CHAPTER 6 Electricity 6-6