Electric Potential
In the previous section of Lesson 1, it was reasoned that the movement of a positive test charge within an
electric field is accompanied by changes in potential energy. A gravitational
analogy was relied upon to explain the reasoning behind the relationship
between location and potential energy. Moving a positive test charge against
the direction of an electric field is like moving a mass upward within Earth's
gravitational field. Both movements would be like going
against nature and would require work by an external force.
This work would in turn increase the potential energy of the object. On the
other hand, the movement of a positive test charge in the direction of an
electric field would be like a mass falling downward within Earth's
gravitational field. Both movements would be like going with
nature and would occur without the need of work by an external force. This
motion would result in the loss of potential energy. Potential energy is the
stored energy of position of an object and it is related to the location of the
object within a field. In this section of Lesson 1, we will introduce the
concept of electric potential and relate this concept to the potential energy
of a positive test charge at various locations within an electric field.
The
Gravitational Analogy Revisited
A gravitational field exists about the Earth that exerts
gravitational influences upon all masses located in the space surrounding it.
Moving an object upward against the gravitational field increases its
gravitational potential energy. An object moving downward within the
gravitational field would lose gravitational potential energy. When gravitational
potential energy was introduced in Unit 5 of
The Physics Classroom, it was defined as the energy stored in an
object due to its 
vertical position above the Earth. The amount of gravitational potential
energy stored in an object depended upon the amount of mass the object
possessed and the amount of height to which it was raised. Gravitational
potential energy depended upon object mass and object height. An object with
twice the mass would have twice the potential energy and an object with twice
the height would have twice the potential energy. It is common to refer to high
positions as high potential energy locations. A glance at the diagram at the
right reveals the fallacy of such a statement. Observe that the 1 kg mass held
at a height of 2 meters has the same potential energy as a 2 kg mass held at a
height of 1 meter. Potential energy depends upon more than just location; it also
depends upon mass. In this sense, gravitational potential energy depends upon
at least two types of quantities:
1)
Mass - a property of the object experiencing the gravitational field, and
2) Height - the location within the gravitational field
So it is improper to refer to high positions within Earth's
gravitational field as high potential energy positions. But is there a quantity
that could be used to rate such heights as having great potential of providing
large quantities of potential energy to masses that are located there? Yes!
While not discussed during the unit on gravitational potential energy, it would
have been possible to introduce a quantity known as gravitational 
potential - the potential energy per kilogram.
Gravitational potential would be a quantity that could be used to rate various
locations about the surface of the Earth in terms of how much potential energy
each kilogram of mass would possess when placed there. The quantity of
gravitational potential is defined as the PE/mass. Since both the numerator and
the denominator of PE/mass are proportional to the object's mass, the
expression becomes mass independent. Gravitational potential is a
location-dependent quantity that is independent of the mass of the object
experiencing the field. Gravitational potential describes the effects of a
gravitational field upon objects that are placed at various locations within it.
If gravitational potential is a means of rating various
locations within a gravitational field in terms of the amount of potential
energy per unit of mass, then the concept of electric potential must have a
similar meaning. Consider the electric field created by a positively charged
Van de Graaff generator. The direction of
the electric field is in the direction that a positive test charge would be pushed;
in this case, the direction is outward away from the Van de Graaff sphere. Work would be required to move a
positive test charge towards the sphere against the electric field. The amount
of force involved in doing the work is dependent upon the amount of charge
being moved (according to Coulomb's law of electric force). The greater the
charge on the test charge, the greater the repulsive force and the more work
that would have to be done on it to move it the same distance. If two objects
of different charge - with one being twice the charge of the other - are moved
the same distance into the electric field, then the object with twice the
charge would require twice the force and thus twice the amount of work. This
work would change the potential energy by an amount that is equal to the amount
of work done. Thus, the electric potential energy is dependent upon the amount
of charge on the object experiencing the field and upon the location within the
field. Just like gravitational potential energy, electric potential energy is
dependent upon at least two types of quantities:
1)
Electric charge - a property of the object experiencing the electrical field,
and
2) Distance from source - the location within the electric
field
While electric potential energy has a dependency upon the charge of the
object experiencing the electric field, electric potential is purely location
dependent. Electric potential is the potential energy per charge.
The concept of electric potential is used to express the
effect of an electric field of a source in terms of the location within the
electric field. A test charge with twice the quantity of charge would possess
twice the potential energy at a given location; yet its electric potential at
that location would be the same as any other test charge. A positive test charge
would be at a high electric potential when held close to a positive source
charge and at a lower electric potential when held further away. In this sense,
electric potential becomes simply a property of the location within an electric
field. Suppose that the electric potential at a given location is 12 Joules per
coulomb, then that is the electric potential of a 1 coulomb or a 2 coulomb
charged object. Stating that the electric potential at a given location is 12
Joules per coulomb, would mean that a 2 coulomb object would possess 24 Joules
of potential energy at that location and a 0.5 coulomb object would experience
6 Joules of potential energy at the location.
Electric Potential in Circuits
As we begin to discuss electric circuits, we will notice that
a battery powered electric circuit has locations of high and low potential. 
Charge moving through the wires of the circuit will encounter changes in
electric potential as it traverses the circuit. Within the electrochemical
cells of the battery, there is an electric field established between the two
terminals, directed from the positive terminal towards the negative terminal.
As such, the movement of a positive test charge through the cells from the
negative terminal to the positive terminal would require work, thus increasing
the potential energy of every Coulomb of charge that moves along this path.
This corresponds to a movement of positive charge against the electric field.
It is for this reason that the positive terminal is described as the high
potential terminal. Similar reasoning would lead one to conclude that the
movement of positive charge through the wires from the positive terminal to the
negative terminal would occur naturally. Such a movement of a positive test
charge would be in the direction of the electric field and would not require
work. The charge would lose potential energy as moves through the external
circuit from the positive terminal to the negative terminal. The negative terminal
is described as the low potential terminal. This assignment of high and low
potential to the terminals of an electrochemical cell presumes the traditional
convention that electric fields are based on the direction of movement of
positive test charges.
In a certain sense, an electric circuit is nothing more than
an energy conversion system. In the electrochemical cells of a battery-powered
electric circuit, the chemical energy is used to do work on a positive test
charge to move it from the low potential terminal to the high potential
terminal. Chemical energy is transformed into electric potential energy within
the internal circuit (i.e., the battery). Once at the high potential
terminal, a positive test charge will then move through the external circuit
and do work upon the light bulb or the motor or the heater coils, transforming
its electric potential energy into useful forms for which the circuit was
designed. The positive test charge returns to the negative terminal at a low
energy and low potential, ready to repeat the cycle (or should we say circuit) all over again.
Check Your Understanding
1. The quantity electric potential is defined as the amount
of _____.
a. electric potential energy
b. force acting
upon a charge
c. potential
energy per charge
d. force per charge
Answer: C
Electric
potential is the amount of potential energy per unit of charge.
2. Complete the following statement:
When
work is done on a positive test charge by an external force to move it from one
location to another, potential energy _________ (increases, decreases) and
electric potential _________ (increases, decreases).
When work is
done on a positive test charge to move it from one location to another,
potential energy increases and electric potentialincreases.
3. The following diagrams show an electric field (represented
by arrows) and two points - labeled A and B
- located within the electric field. A positive test charge is shown at point
A. For each diagram, indicate whether work must be done upon the charge to move
it from point A to point B. Finally, indicate the point (A or B) with the
greatest electric potential energy and the greatest electric potential.
|
Work done on charge? Electric PE is greatest at: Electric potential is greatest at: |
Work done on charge? Electric PE is greatest at: Electric potential is greatest at: |
|
Work done on charge? Electric PE is greatest at: Electric potential is greatest at: |
Work done on charge? Electric PE is greatest at: Electric potential is greatest at: |
Yes
|
Work done on
charge? (The +
charge is moving with nature; work is not required when it moves
with the E field.) Electric PE
is greatest at: (When a +
charge moves naturally in the direction of the E field, it is moving from
high PE to low PE. So the charge has a higher PE at A.) Electric
potential is greatest at: (For the
same charge, the electric potential is greatest at locations of higher
potential energy.) |
Work done on
charge? (The +
charge is moving against nature; work is required to move it
against the E field.) Electric PE
is greatest at: (When work
is done to move an object against nature, the PE of the object increases. So
the charge possess more PE when at B.) Electric
potential is greatest at: (For the
same charge, the electric potential is greatest at locations of higher
potential energy.) |
|
Work done on
charge? (The +
charge is moving with nature; work is not required when it moves
with the E field.) Electric PE
is greatest at: (When a +
charge moves naturally in the direction of the E field, it is moving from
high PE to low PE. So the charge has a higher PE at A.) Electric
potential is greatest at: (For the
same charge, the electric potential is greatest at locations of higher
potential energy.) |
Work done on
charge? (The +
charge is moving against nature; work is required to move it
against the E field.) Electric PE
is greatest at: (When work
is done to move an object against nature, the PE of the object increases. So
the charge possess more PE when at B.) Electric
potential is greatest at: (For the
same charge, the electric potential is greatest at locations of higher
potential energy.) |