Transcript Electric Potential Energy

2/20 Do now
• What is electric energy?
• What is electric potential?
Due:
18.1-2 notes
Assignment:
Castle learning
objective
1. Define electric potential energy
2. Distinguish between electrical potential
energy, electric potential, and potential
difference
3. Compute the electric potential for various
charges distributions.
Electric Potential Energy
• Electric potential energy are similar to gravitational potential energy both involve field forces.
Gravitational potential
energy is a result of
interaction between masses.
It depends on the mass and
the field strength and the
relative position.
PEg = mg∆h
Similarly, electric potential
energy is a result of
interaction between
charges. It depends on the
charge and field strength
and relative position.
-
High PE
Work done by
electric field
High PE
Work done by
external force
Low PE
-
Low PE
++++++++++++
Moving the + test charge against
the E field from A to B will
require work and increase the
potential energy of the charge.
This is similar to an object going
uphill.
The + test charge will naturally
move in the direction of the E field
from B to A; work is not required.
The potential energy of the charge
will decrease. This is similar to an
object going downhill.
Electric energy of the test charge depends on its charge q, the
electric field strength E and its position.
Energy is conserved
• Electric energy can be produce from many sources and also
can be converted into other types of energy. Electric
potential energy is a form of mechanical energy:
TME = KE + PEg + PEs + PEe
+
+
+
+
d
-
• In a uniform field, when a charge is released, work done by
the field on the charge equals to its lose PE e and it gain in
KE because there is no friction.
1 2
W  F  d  q  E  d  PEe  KE  mv
2
The Gravitational Potential
GPE = mgh
gh, is a quantity that could be used
to rate various locations about the
surface of the planet in terms of
how much potential energy each
kilogram of mass would possess
when placed there.
gh, is known as gravitational potential.
GPE
gh 
m
Gravitational potential is defined as the PE/mass. It is mass
independent. Gravitational potential describes the affects of a
gravitational field upon objects that are placed at various locations
within it.
• Electric potential (V) is defined as potential energy per
charge.
• Electric potential is a property of the
PEe
location within an electric field. Electric
V
potential (V) does not depend on q.
q
The electric potential is
the same for all charges
at a given location. A
test charge with twice the
quantity of charge would
possess twice the
potential energy at that
location.
Electric Potential Difference
• Electric potential difference between point A and point B is the
change is potential between point A and B
PEB PEA W
V  VB  VA 


q
q
q
B
+e
A
The standard metric unit on electric potential difference is the
volt or voltage. 1 Volt = 1 Joule / Coulomb.
If 1 joule of work is needed to move 1 C of charge from point A to
point B, the potential difference between point A & B is 1 Volt.
If 3 joule of work is needed to move 1 C of charge from point A to
point B, the potential difference between point A & B is 3 Volts
Storing Electrical
Energy
4.1.5 Electrical Potential (Voltage)
Electrical PE
To increase PE
+
+
-
+
-
+
To decrease PE
+
+
Calculating Potential Difference
• Amount of potential difference:
• WORK DONE PER UNIT CHARGE
• 1 VOLT = 1 J/C
W
V 
q
Example #1
• 6.0 joules of work are done in pushing an object with
+3.0 coulombs of charge toward a charged plate.
– What type of charge does the plate have on it?
– How much potential energy was stored in the electric fields?
– How much electrical potential was generated?
Positive
6.0 J
V = W/q
V = 6.0 J / 3.0 C
V = 2.0 V
Example #2
• An object with a 2.0 coulomb charge is accelerated
through a potential difference of 10 volts.
– How much kinetic energy does the object gain?
V = W/q
W = Vq
W = (10 V)(2.0 C) = 20 J
Electron-volts
• Alternate unit for work/energy:
• Raises 1e to an electrical potential of 1 V
• 1 eV = 1.6 x 10-19 J
What is
is the
the energy
energy needed
needed to
to raise
raise four
two
What
electronsto
toaapotential
potentialof
of2.5
1.0volts?
volt?
electrons
V = W /q
1.0 V = W / 4e
2.5
2e
W = 2.0eV
10 eV
Example #3
• An electron travels a distance of 2.0 x 10-3 meter as its
electrical potential is raised by 300 volts.
– How much work is done on the electron?
V = W/q
V = W/q
300 V = W / 1e
300 V = W / 1.6 x 10-19 C
W = 300 eV
W = 4.8 x 10-17 J
End of 4.1.5 - PRACTICE
Electric Potential in Circuits
A battery powered electric circuit has locations of high and low
potential.
Within the cells of the battery, the electric field is directed from the
positive terminal towards the negative terminal. As a positive test
charge move through the cells from the negative terminal to the
positive terminal, it would require work, thus the potential energy
of the charge would increase. It is for this reason that the positive
terminal is described as the high potential terminal.
• As a positive charge move through the wires from
the positive terminal to the negative terminal, it
would move in the direction of the electric field and
would not require work. The charge would lose
potential energy. The negative terminal is described
as the low potential terminal.
Equipotential lines
• Equipotential lines connect positions of which has the
same potential energy. As a charge moves along an
equipotential line, there is no change in potential
difference and potential energy, the work is not done
on the charge. As the charge crosses equipotential
lines, the potential energy changes.
++++++++++++++++++++++++++++++
+e
+e
------------------------------------------------------
example
• How many eV is required to move 3.2 x 10-19 C
of charge through a potential difference of 5.0
volts?
V=W/q
5.0 V = W / (3.2 x 10-19 C) = W / (2 elem. Charges)
W = 10 eV
example
•
Moving +2.0 coulombs of charge from infinity
to point P in an electric field requires 8.0 joules
of work. What is the electric field potential at
point P?
The electric potential at any point in an electric field is
the work required to bring a unit positive charge from
infinity to that point.
V = W / q = 8.0 J / (2.0 C) = 4.0 V
example
• The graph shows the relationship between
the work done on a charged body in an
electric field and the net charge on the
body. What does the slope of this graph
represent?
Slope = rise / run
Slope = W / q = V
The slope represent the
potential difference.
Lab 20: E-field PhET lab
Purpose:
1. investigate electric field created by a positive charge, a negative
charge, and both charges at the same time
2. investigate how the magnitude of electric field relates to the
distance from the source charge.
Material: Computer, Internet
Procedure: go to
http://phet.colorado.edu/en/simulation/charges-andfields; follow instructions on the lab directions.
Conclusion: answer questions indicated in the purpose.
Lab write up
•
should include title, purpose, material, answer all the questions,
fill in the data tables and write conclusions as indicated in the
lab directions sheet.
• Moving 2.0 coulombs of charge a distance
of 6.0 meters from point A to point B within
?
an electric field requires a 5.0-N force.
What is the electric potential difference
between points A and B?
objectives
Know:
- Definition of electrical potential; electron-volt
- Unit of electrical potential
- Electrical potential equation
Understand:
- How energy is stored in electric fields.
- Relationship between electrical potential, work, and charge.
- Appropriateness of using electron-volts vs. joules.
Be able to:
- Use the electrical potential equation to:
• Solve for unknown variables.
• Find kinetic energy
- Determine methods for maximizing or minimizing electrical
potential.
- Convert from electron-volts to joules.