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 energy2. 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.

-

-

Work done by electric field

Work done by external force

Low PE

High PE

Low PE

High PE

PEg = mg∆h

Gravitational potential energy is a result of interaction between masses. It depends on the mass and the field strength and the relative position.

Similarly, electric potential energy is a result of interaction between charges. It depends on the charge and field strength and relative position.

+ + + + + + + + + + + +

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.

• 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

• 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.

2

21 mvKEPEdEqdFW e

d

----

++++

Energy is conserved

The Gravitational PotentialGPE = mghgh, 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.

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.

gh, is known as gravitational potential. mGPEgh

• Electric potential (V) is defined as potential energy per charge.

qPEV e

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 is a property of the location within an electric field. Electric potential (V) does not depend on q.

• Electric potential difference between point A and point B is the change is potential between point A and B

Electric Potential Difference

qW

qPEA

qPEVVV B

AB

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

A

B

+e

Storing Electrical Energy

4.1.5 Electrical Potential (Voltage)

To increase PE

+ +

To decrease PE

+-

Electrical PE

+ + +-

qWV

Calculating Potential Difference• Amount of potential difference:

• WORK DONE PER UNIT CHARGE• 1 VOLT = 1 J/C

• 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

Example #1

6.0 J

V = W/q

V = 6.0 J / 3.0 C

V = 2.0 V

• 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?

Example #2

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 the energy needed to raise two electrons to a potential of 1.0 volt?

V = W /q

1.0 V = W / 2e

W = 2.0eV

What is the energy needed to raise four electrons to a potential of 2.5 volts?

V = W /q

2.5 V = W / 4e

W = 10 eV

• 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?

Example #3

V = W/q

300 V = W / 1e

W = 300 eV

V = W/q

300 V = W / 1.6 x 10-19 C

W = 4.8 x 10-17 J

End of 4.1.5 - PRACTICE

Electric Potential in CircuitsA 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

++++++++++++++++++++++++++++++

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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 labPurpose: 1. investigate electric field created by a positive charge, a negative

charge, and both charges at the same time2. investigate how the magnitude of electric field relates to the

distance from the source charge.Material: Computer, InternetProcedure: go to

http://phet.colorado.edu/en/simulation/charges-and-fields; 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.