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The potential difference can be measured by the work that is

done to move the charge or by the work that the charge can do because

of its position in the fi eld. This is perfectly analogous to the work
that must be done to give an object gravitational potential energy
or to the work that the object can potentially do because of its new

position. Thus, when a 12 volt battery is charging, 12.0 joules of
work are done to transfer 1.00 coulomb of charge from an outside
1.00 1.00 source against the electric field of the battery terminal. When the

coulomb coulomb 12 volt battery is used, it does 12.0 joules of work for each coulomb
(+)
(+)
(+) (+)
of charge transferred from one terminal of the battery through the
electrical system and back to the other terminal.
1.00 joule 6.2 ELECTRIC CURRENT
of work
So far, we have considered electric charges that have been instan-
taneously moved by friction but then generally stayed in one
FIGURE 6.8 Electric potential results from moving a positive place. Experiments with static electricity played a major role in
coulomb of charge into the electric field of a second positive coulomb
the development of the understanding of electricity by identify-
of charge. When 1.00 joule of work is done in moving 1.00 coulomb
of charge, 1.00 volt of potential results. A volt is a joule/coulomb. ing charge, the attractive and repulsive forces between charges,

and the field concept. Now, consider the flowing or moving of
charge, an electric current (I). Electric current means a fl ow of

of Earth. Likewise, an electric charge has an electric fi eld sur- charge in the same way that water current means a flow of water.

rounding it, and work must be done to move a second charge into Since the word current means flow, you are being redundant if

or out of this field. Bringing a like charged particle into the fi eld you speak of “flow of current.” It is the charge that fl ows, and

of another charged particle will require work since like charges current is defined as the flow of charge.
repel. Separating two unlike charges will also require work since
unlike charges attract. In either case, the electric potential energy THE ELECTRIC CIRCUIT
is changed, just as the gravitational potential energy is changed by
When you slide across a car seat, you are acquiring electrons
moving a mass in Earth’s gravitational fi eld.
on your body by friction. Through friction, you did work on

One useful way to measure electric potential energy is to con-
the electrons as you removed them from the seat covering. You
sider the potential diff erence that occurs when a certain amount of
now have a net negative charge from the imbalance of electrons,
work is used to move a certain quantity of charge. For example,
which tend to remain on you because you are a poor conductor.
suppose there is a firmly anchored and insulated metal sphere

But the electrons are now closer than they want to be, within a
that has a positive charge (Figure 6.8). The sphere will have a

repulsive electric field, and there is an electrical potential diff er-
positive electric field in the space around it. Suppose also that you

ence between you and some uncharged object, say, a metal door
have a second sphere that has exactly 1.00 coulomb of positive
handle. When you touch the handle, the electrons will fl ow, cre-
charge. You begin moving the coulomb of positive charge toward
ating a momentary current in the form of a spark, which lasts

the anchored sphere. As you enter the electric field, you will have
only until the charge on you is neutralized.
to push harder and harder to overcome the increasing repulsion.
To keep an electric current going, you must maintain the
If you stop moving when you have done exactly 1.00 joule of
separation of charges and therefore maintain the electric fi eld
work, the repulsion will do 1.00 joule of work if you now release
(or potential difference), which can push the charges through a

the sphere. The sphere has potential energy in the same way that

conductor. This might be possible if you could somehow contin-

a compressed spring has potential energy. In electrical matters,
uously slide across the car seat, but this would be a hit-and-miss
the potential diff erence that is created by doing 1.00 joule of work in
way of maintaining a separation of charges and would probably

moving 1.00 coulomb of charge is defined to be 1.00 volt. Th e volt (V)
result in a series of sparks rather than a continuous current. Th is
is a measure of potential difference between two points, or

is how electrostatic machines work.
work to create potential
__ A useful analogy for understanding the requirements for

electric potential difference =
charge moved a sustained electric current is the decorative waterwheel device
(Figure 6.9). Water in the upper reservoir has a greater gravita-
W _
V = tional potential energy than water in the lower reservoir. As water

q
flows from the upper reservoir, it can do work in turning the

equation 6.3 waterwheel, but it can continue to do this only as long as the pump
does the work to maintain the potential difference between the two

In units,

reservoirs. This “water circuit” will do work in turning the water-
1.00 joule (J)
__ wheel as long as the pump returns the water to a higher potential
1.00 volt (V) =

1.00 coulomb (C) continuously as the water flows back to the lower potential.
146 CHAPTER 6 Electricity 6-8