Name ______________________________________ Date ____________ Per ______
Electric Potential
We have spent some time talking about the Electrostatic Force that exists between two
charged particles, and how it is that this force relates to and is caused by the Electric Field. It
is not difficult to show that the farther apart the two charges are, the weaker the force
becomes. However, in order to move the charges apart, some amount of work must be done
on the particles. The work done on the charges is converted to electrical potential energy.
This is a very similar concept to gravity. As you do work on an object to lift it (i.e., separate it
from the earth) that work is converted to gravitational potential energy.
Gravitational Potential
The amount of PEg that something has is determined by two factors: the height, and the mass.
If two different objects are lifted to the same height h, then the mass is the variable that will
determine how much PEg an object will have.
We can define a term known as the gravitational potential, a quantity that will give us the
amount of PEg an object has with respect to its mass. This gravitational potential would be
equal to the gravitational potential energy divided by mass. In other words,
Gravitational Potential = Mgh
M
or
Gravitational Potential = g*h
Gravitational Potential is in essence the amount of gravitational potential energy per unit
mass that any object will have at a height h. The gravitational potential is determined solely
by the physical environment and is not dependent on the individual mass. This indicates
that, for a given height, we can determine the amount of potential energy that any mass will
have. While the amount of Gravitational Potential Energy is different for each mass at that
height, the Gravitational Potential is the same for all masses at that height. The key idea
here is that the amount of gravitational potential energy is equal to the mass times the
gravitational potential.
Electric Potential Notes
Bradshaw
Name ______________________________________ Date ____________ Per ______
Electric Potential
There is a similar concept in the field of Electrostatics. When two charges are separated from
one another, there is a certain amount of electrical potential energy inherent to the system.
We can define a term known as Electric Potential (V) as the amount of electrical potential
energy a certain charge has divided by that charge. In other words,
Electric Potential = Electric Potential Energy
Charge
V = PEE
Q
**Note: We commonly use the term Voltage in place of Electric Potential. **
Please consult the following visual aid:
The picture on the left shows two different masses (m and 2m) elevated to the same height
h. The two objects have different masses, and hence they have different values of PEg;
however, they have an identical amount of gravitational potential (g*h is the same for both
masses)..
The picture on the right shows two different charges (q and 2q) that are placed in an identical
electric field. They have different amounts of electrical potential energy due to the different
amounts of charge, but they have the same Electric Potential.
In each of the diagrams above, the difference in Potential from the top to the bottom is
simply the strength of the field between those two points (g on the left; E on the right)
multiplied by the distance the object would move through that field (h on the left; d on the
Electric Potential Notes
Bradshaw
Name ______________________________________ Date ____________ Per ______
right).
*Note that, in the diagram on the left (gravity), the masses will want to move from a point of
higher potential (top) to lower potential (bottom). Essentially, we can say that an object
“wants” to be in a position where it has less gravitational potential energy. This is similar
with Electrical charges; however, due to polarity differences, we have to be very careful. We
say that a positive charge will want to move from a point of higher potential (+ charge) to a
point of lower potential (- charge). A negative charge will want to go from a lower potential
to a higher potential. This should not be terribly surprising; we are basically saying that a
charge will have a tendency to move in the direction of the electrostatic force acting on it
(much as a mass will fall because gravity pulls it downwards).
Electric Potential Notes
Bradshaw
Name ______________________________________ Date ____________ Per ______
Electric Potential
Electric Potential is measured in units called Volts (V). Electric Potential is often referred to
by other names. We will most often be concerned with the difference in potential between
two points; as such, we can also use the term Potential Difference. It is simply called
Potential, and is most commonly referred to as Voltage. We will use these terms
interchangeably in class.
We will consider Electric Potential in two separate scenarios:
1.
Parallel Plate Capacitor – As shown above, where d is the distance between the
plates and E is the electric field between the plates. We say that this V is the
“Voltage across the plates”; it literally describes the difference in electric potential
between the + and - plates.
2.
Potential a distance from a single charge – Much like electric fields, there is a certain
Potential due to the presence of an electric charge. To find the Electric Potential V a
distance R from a charge q:
Electric Potential is a scalar; this indicates that there is no direction to consider. However, it
is sign-sensitive; it is possible to have a negative electric potential. Since we will most often
be concerned with the difference in potential between two points, this can certainly be a
negative number.
Electric Potential Notes
Bradshaw