down the hill (or the test charge is allowed to coast back to plate A), its potential energy
decreases.
Now we discuss the same points, using equations. Electric potential can be calculated
as the electric potential energy created by placing a test charge in a field, divided by the
test charge. The electric potential difference is the change (difference) in electric
potential energy divided by the test charge. These two equations are shown in Concept
What causes this change in potential energy? The work done on the system. Taking the
previous equation and replacing ǻPE with work W,we find that the electric potential
difference is W/q, or work per unit charge. This is shown in Concept 2.
In all this discussion, a positive test charge has been used. This is the standard way to
determine the electric potential. However, negative charges (like electrons) can move,
too. When free to move, a negative charge will naturally move to an area of higher
potential (the positive plate in this example). This will decrease the system’s potential
energy. With positive work, it can be forced to return to the negative plate, and this will
increase the potential energy of the system. (As a form of shorthand, you may
sometimes see this referred to as the PE of the charge, but it is important to remember
that the charge only has PE because of the field caused by other charges.)
The electron volt, a common unit of energy in many areas of physics study, is based on
the relationship of energy, charge and potential difference. One electron volt (eV)
equals the change in the potential energy of an elementary charge (1.60×10í^19 C) when
it moves through a potential difference of one volt. We can use a rearrangement of the
second equation in Concept 1, ǻPEe = qǻV, to calculate that an electron volt equals
1.602 18×10í^19 J. Note that the electron volt equals charge multiplied by electric
potential, which equals electric potential energy. In spite of its name this unit refers to
electric potential energy, not electric potential as volts do.
PE, work and potential difference
W = ǻPEe , so
ǻV = W/q
What is the potential difference
between the plates?
W = Fǻx
ǻV = W/q
ǻV = Fǻx/q
ǻV = (3.0 N)(5.0 ȝm)/(7.5 ȝC)
ǻV = 2.0 V
24.8 - Interactive checkpoint: lead acid cell
A typical car battery consists of six
lead-acid cells. Each cell has a
potential difference of 2.05 V across
it. The negative electrode is at a
potential of í1.685 V, while the
positive electrode is at a potential of
+0.365 V. What is the change in
electric potential energy for one
electron that is moved from the
positive to the negative electrode of
one of the cells?
Answer:ǻPEe = J