Because the electric force can displace charged objects,
it is capable of doing work. The presence of an electric field implies
the potential for work to be done on a charged object. By studying
the electric potential between two points in an electric
field, we can learn a great deal about the work and energy associated
with electric force.
Electric Potential Energy
Because an electric field exerts a force on any charge
in that field, and because that force causes charges to move a certain
distance, we can say that an electric field does work on charges.
Consequently, we can say that a charge in an electric field has
a certain amount of potential energy, U.
Just as we saw in the chapter on work, energy, and power, the potential energy
of a charge decreases as work is done on it:
The work done to move a charge is the force, F
exerted on the charge, multiplied by the displacement, d
of the charge in the direction of the force. As we saw earlier,
the magnitude of the force exerted on a charge q
an electric field E
is = qE
Thus, we can derive the following equation for the work done on
Remember that d is not simply
the displacement; it is the displacement in the direction that the
force is exerted. When thinking about work and electric fields,
keep these three rules in mind:
When the charge moves a distance r parallel
to the electric field lines, the work done is qEr.
the charge moves a distance r perpendicular
to the electric field lines, no work is done.
the charge moves a distance r at an
angle to the electric field lines, the work done
is qEr cos .
an electric field, E,
a positive charge, q, is moved in the circular
path described above, from point A to point B,
and then in a straight line of distance r toward
the source of the electric field, from point B to
point C. How much work is done by the electric
field on the charge? If the charge were then made to return in a straight
line from point C to point A,
how much work would be done?
How much work is done moving the charge from point A to
point B to point C ?
The path from point A to
point B is perpendicular to the radial
electric field throughout, so no work is done. Moving the charge
from point B to point C requires
a certain amount of work to be done against the electric
field, since the positive charge is moving against its natural tendency
to move in the direction of the electric field lines. The amount
of work done is:
The negative sign in the equation reflects the fact that
work was done against the electric field.
How much work is done moving the charge directly
from point C back to point A?
The electric force is a conservative force, meaning that
the path taken from one point in the electric field to another is
irrelevant. The charge could move in a straight line from point C to
point A or in a complex series of
zigzags: either way, the amount of work done by the electric field
on the charge would be the same. The only thing that affects the
amount of work done is the displacement of the charge in the direction
of the electric field lines. Because we are simply moving the charge
back to where it started, the amount of work done is W
Much like gravitational potential energy, there is no
absolute, objective point of reference from which to measure electric
potential energy. Fortunately, we are generally not interested in
an absolute measure, but rather in the electric potential, or potential
difference, V, between two
points. For instance, the voltage reading on a battery tells us
the difference in potential energy between the positive end and
the negative end of the battery, which in turn tells us the amount
of energy that can be generated by allowing electrons to flow from the
negative end to the positive end. We’ll look at batteries in more
detail in the chapter on circuits.
Potential difference is a measure of work per unit charge,
and is measured in units of joules per coulomb, or volts (V).
One volt is equal to one joule per coulomb.
Potential difference plays an important role in electric
circuits, and we will look at it more closely in the next chapter.