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Electric Potential
Review: Work and Energy
Work is defined as the product of
force F times displacement d.
Work = F x d; Units: Joules
Potential Energy is defined as the ability to do work
by virtue of position or condition. (Joules)
Once again, we’ll use gravity as
an analogy…
Work in a gravitational field
• When gravity does work on an object to move it in
the direction of the gravitational field, then the object
loses potential energy.
• On the other hand, energy would be required to move
a massive object against a gravitational field. Energy
in the form of work would have to be imparted to the
object by an external force in order for it to gain this
height and the corresponding potential energy.
Work (as applied to gravity)
• The important point to be made by this gravitational analogy is
that work must be done by an external force to move an object
against nature - from low potential energy to high potential
energy.
• On the other hand, objects naturally move from high potential
energy to low potential energy under the influence of the field
force. It is simply natural for objects to move from high energy
to low energy.
Another example…
In which drawing does the bow have more
potential energy?
Was an external force required to get the bow to
a position of higher potential energy?
Work in an Electric Field
• In a similar manner, to move a charge in an electric field
against its natural direction of motion would require work. The
exertion of work by an external force would in turn add
potential energy to the object.
• The natural direction of motion of an object is from high
energy to low energy; but work must be done to move the
object against nature.
• On the other hand, work would not be required to move an
object from a high potential energy location to a low potential
energy location. The field itself does that!
Consider the diagram above in which a positive source
charge is creating an electric field and a positive test
charge is being moved against and with the field.
In Diagram A, the positive test charge is being moved
against the field from location A to location B. Moving
the charge in this direction would be like going against
nature. Thus, work would be required to move the
object from location A to location B and the positive
test charge would be gaining potential energy in the
process. This would be analogous to moving a mass in
the uphill direction; work would be required to cause
such an increase in gravitational potential energy.
In Diagram B, the positive test charge is being moved
with the field from location B to location A. This
motion would be natural and not require work from
an external force. The positive test charge would be
losing energy in moving from location B to location A.
This would be analogous to a mass falling downward;
it would occur naturally and be accompanied by a
loss of gravitational potential energy.
The high energy location for a positive test charge is
a location nearest the positive source charge; and the
low energy location is furthest away.
What is the source charge is negative?
The low energy location for a positive test charge is a location
nearest a negative source charge and the high energy location is
a location furthest away from a negative source charge.
Check your understanding:
Electrical potential energy is the energy a
charged object has due to its
a. movement in an electric field.
b. energy.
c. position in an electric field.
Check your understanding:
If a small positive charge is brought near a large, positively
charged conductor, what happens to its electrical potential
energy?
a. Because the charges are the same the energy is reduced.
b. Because they repel, its potential energy will increase.
c. Because the charges are the same, the energy will not be
changed.
1.
Is the source charge positive or negative? How do you know?
2.
If you pushed a positive test charge in the direction of the blue arrow,
would it take work?
3.
If you pushed the positive test charge in the direction of the blue arrow,
would it gain or lose electric potential energy?
4.
What would happen if you released the charge after pushing it toward the
center?
Electric Potential
Consider the electric field created by this large positive charge. 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 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
depends on the amount of charge being moved. 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.
So far we’ve talked about
Electric Potential Energy, but
Electric Potential isn’t quite
the same thing.
Electric Potential
•Electric potential energy depends on the
charge of the object experiencing the
electric field. The greater the charge on the
“test charge,” the greater the electric
potential energy.
•To continue the gravity analogy, a boulder
sitting on top of a cliff has more potential
energy than a pebble sitting at the same
spot.
Electric Potential
•Electric potential is purely location
dependent. Electric potential is the
potential energy per charge.
Check your understanding:
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).
Answer the questions for each
diagram:
•Is work required to move the test charge
from point A to point B? _____
•Does the test charge gain or lose
potential energy? __________________
•Which point (A or B) has the greatest
electric potential? _____potential.
True or False?
• Electric potential at a point is a property
of the space, whereas electric potential
energy cannot exist unless a charge is
placed at that point.
The SI Unit of Potential (Volt)
From the definition of electric potential as P.E.
per unit charge, we see that the unit must be
J/C. We redefine this unit as the volt (V).
A potential of one volt at a given point means that
a charge of one coulomb placed at that point will
experience a potential energy of one joule.
CONCLUSION:
Electric Potential