1. Electrical Energy Fields
Or Fields of Dreams 2
Standards:
5j* Students know electric and magnetic fields contain energy and act as vector force fields.
5o* Students know how to apply the concepts of electrical and gravitational potential energy to solve problems involving conservation of energy.

2. An electric charge changes the space around it so that other charges…
Feel an electrical force
Electrical force field
Measured by electrical force (FE) and electrical field (E)
Vector quantities and addition
Have an electrical potential energy
Electrical energy field
Measured by electrical potential energy (PEE) and Electrical potential (V) aka potential aka voltage
Scalar quantities
All assume a positive test charge
Questions: How does an electrical charge change the space around it?
None, this is a review slide

3. Measuring the Electric Energy Field
Electrical Potential Energy (PEe) is a scalar quantity that measures the electric energy field around a charge in joules
Electrical Potential aka Potential aka Voltage (V) is a scalar quantity measuring the electric energy field in Joules/Coulomb or Volts.
Both vary with source charge and distance from the source charge but only electrical potential energy varies with test charge.
PEe = Qtest V
Question: What two variables are used to measure the electrical energy field around a charge? How are these quantities similar and how do they differ? How do they differ from the electrical force variables?
Activities:
Start with large source charge on board and talk about how want to map the energy field around it. Can be done by placing charge at different positions and measuring how much potential energy it has. Problem is that each point will have different number depending on source charge. Can create a new variable that is independent of test charge by dividing potential energy by test charge. We call this variable electrical potential or potential or voltage.
Make chart on board for electrical potential energy and Voltage/Electrical Potential/Voltage listing both as measuring electric energy field, being scalar quantities and their units. Go through math and explanation of how both vary with distance and source charge but by defining V = PE/Q only the PE will vary will source charge.
Add the force variables to your chart and discuss how V and E are similar and how PE and F are similar. The point out differences in two fields including one is a vector and the other a scalar field. Write two equations relating force and energy variables.

4. Check Question
Do a or b have the greater electrical PE? How about Voltage?
Do b or c have the greater electrical PE? How about Voltage A C B

5. Representing Electrical Energy Fields
Equipotential line diagram has closed loops connecting points of equal electrical potential or potential or voltage.
Lines are perpendicular to force lines
Faraday diagram treats equipotential lines as elevations and equates gravitational and electrical potential.
Positive point charge = hill, negative=hole
Positive plate = plateau, negative plate=linear valley
Questions: What is an equipotential line? How do these lines relate to the force field lines? How did Faraday interpret equipotential lines in his diagrams? Describe the Faraday diagrams for the following charge distributions: a) positive point charge b) negative point charge c) positive plate charge d) negative plate charge.
Activities:
Make chart listing charge distribution, equipotential diagram and Faraday diagram for point and plate charges.
Draw equipotential diagrams. Point out that these lines are perpendicular to force lines from before.
State that equipotential diagrams don’t usually mean a whole lot to people. State Faraday diagrams equate electric potential with elevation. Draw the diagrams in chart. Now can see what an electrical test charge sees and how it will respond simply by remembering the observation that things roll down hill. Try a couple questions along the lines of which direction charge will move.

6. Check Question Which charge has the stronger electric field?
Which charge is positive?
Which direction would a proton move if placed between the charges? A 5 10 B
-10 -5

7. Energy Conservation
Potential energy defined to be zero an infinite distance away from plate
Positive Plate or Point
PEe and V are positive and decrease as charge moves away from source charge.
KE is positive and increases as charge moves away from plate.
PE vs. Position Graph is hyperbola in 1st quadrant
Negative Plate or Point
PE and V are negative and decrease in absolute value as charge moves away from source charge.
KE is positive and increases as moves away from plate
PE vs. Position Graph is hyperbola in 4th quadrant
Conservation of energy
PE + KE =ME = Constant
KE + velocity same when ever charge at same x PE
Questions: By convention where is the electrical potential energy defined to be zero for a single plate or point charge? As you move nearer the source charge what happens to the absolute value of the electrical potential energy, electric potential aka voltage and kinetic energy? If a test charge is displaced from its initial position a force so it has a larger PE, how is the KE when it returns to its original position related to this new PE?
Activities:
1) Draw two types of plate charges and point out that force on charge is in opposite directions. State that by convention PE and V are considered to be zero at a location an infinite distance from the plates.
2) Discuss how charge moving in opposite charge fields will increase KE and decrease PE when moving outward. Draw PE vs. x graph to show this.
3) For Physics E discuss how get same thing as above if let PE start out at large negative number for like charged plate and test charge. Draw graph and discuss how absolute value of PE decreases as move away from plate while KE increases.
4) Discuss how ME remains same and thus any work done by a force to change the PE becomes KE when charge returns to initial position before displacement.
5) Charge originally moving towards or away from plate and then returning back to initial position will have same KE and PE moving inward or outward x

8. Check Question
It takes 100 joules of work to push a test charge 2 cm closer to a positive plate. The charge is then released.
What is the potential energy change of the charge after the push?
What is the potential energy change of the charge when it returns to its initial position?
What is the kinetic energy of the charge when it returns to its initial position?
What is the velocity of the charge when it returns to its initial position if its mass is 2 kg?

9. Opposite Point Charges
Electric Potential Energy and Electrical Potential/Potential/ Voltage all decrease as move away from positive charge and towards negative charge
Kinetic energy increases as move towards negative charge
Faraday diagram is a hill and hole
PEelectric =S Kc QsourceQtest /d
V= PEelectric /Qtest = SKc Qsource /d
Source charges not always equal
Question: Draw the equipotential and Faraday diagrams for opposite point charges. How do the electrical potential, electrical potential energy and kinetic energy of a test charge change as it moves away from the positive and towards the negative charge? Write the equations for finding the electrical potential energy and electrical potential in this field.
Activities:
Draw equipotential and then Faraday diagram of this situation.
Discuss energy and potential as move from positive to negative charge. Discuss how conservation of energy plays out.
Write equations and explain each term. Discuss how can have higher hill or deeper hole depending on size of charges.

10. Opposite Plate Charges
Electrical potential energy and electrical potential decrease as test charge moves from positive to negative plate
Faraday diagram is inclined plane sloping down towards negative plate
V = PE/Qtest, V=Ed and Q=CV
Method of storing electric energy
Question: Draw the equipotential and Faraday diagrams for opposite plate charges. How do the electrical PE, potential and kinetic energy of a particle vary between the two plates? What equations apply to this charge distribution?
Activities:
Draw equipotential and Faraday diagrams for oppositely charged plates and number the field lines
Comment on how PE and V decrease as charge moves towards negative plate, while KE of charge will increase
State that for this arrangement and only for this arrangement V=Ed and PE = Fd where d is distance from negative plate
Talk about how this arrangement is used to store electrical energy and is called a capacitor

11. Van de Graaff Generator
Lightning rods leak charge onto belt which transfers and leaks charge onto second set of points which conduct charge to large ball which is insulated from ground.
Ball can hold enormous amounts of charge before lightning discharge
Light held perpendicular to surface lights because of difference in PE, V, FE and E
Shock occurs when charge allowed to reach Earth
Question: Describe how a Van de Graaff generator builds up charge. Explain why a fluorescent light bulb will light up when it is perpendicular to the surface of the conducting sphere but not parallel.
Activities:
Show that Van de Graaff can demonstrate that opposites attract with pie pans, mop head and puffed rice.
Show that lights up bulb when perpendicular not parallel. Discuss how there is a difference in the electric force, field, PE and potential in former case. Thus is takes a DIFFERENCE in these to move charge.
Finish by sticking long haired blonde child on insulated stool and charging hair then shock class while holding hands and touching charged student. Point out that trick to keeping from being shocked is to NOT allow charge to reach ground. So if all are insulated we are safe.
Finally point out that Van de Graaff produces Volts but we are not all dead. Reason is that although the difference in force, field, PE and voltage are large the actual number of electrons moving through us is small. Like the sparks from a sparkler, yes each spark has a lot of energy but there are so few of them that the amount of you that is burned is small.

12. Check Question
Explain why the fluorescent lamp will light up when it is perpendicular to the charged Van de Graaff sphere’s surface but NOT when it is parallel?
What is the electric energy field inside the sphere?

13. Electrical Energy Field Variables
Electrical PE (PEe)
Electrical Potential, Potential or Voltage (V)
Potential Energy charge has due to its position near another electrical charge
Units of Joules
Scalar quantity
Usually measured relative to a reference value
DPEE = Qtest DV
Varies w/ test charge, source charge and distance
Potential energy for each coulomb of charge due to test charge’s position near another electrical charge
Units of Joules/ Coulomb or Volts
Scalar quantity
Usually measured relative to a reference value
DV = DPEE / Qtest
Varies w/ source charge and distance only
Questions: What two variables measure the electrical energy field around a charge? What is the definition of each, what units are each measured in and are they scalar or vector quantities? With what variables does each vary? Write an equation that connects these two variables.

14. Representing Electrical Energy Fields
Equipotential Diagrams
Equipotential lines connect locations of equal potential energy
Equipotential lines never cross one another
Close equipotential lines indicate strong fields
Test charges move from high to low potential
Lines are perpendicular to force lines
Faraday Diagrams
Equate potential to elevation like on contour map
Test charges roll downhill
Positive points are hills, Negative points are holes, positive plates are plateaus and negative plates linear valleys.
Question: What type of diagram is used to represent electrical fields. How does the diagram indicate the strength of the field? In which direction will test charges move in comparison to the equipotential lines? How do the directions of equipotential and force lines compare? What do Faraday diagrams equate the equipotential lines to?

15. Examples of Energy Fields
Point Charges
Equipotential diagrams
Faraday diagrams
Equations
DPEE = Kc Qsource Qtest/d
DV= Kc Qsource /d
Opposite Plate Charges
Diagrams
Potential decreases as move towards negative plate in linear fashion
DV=E Dd only for this case (uniform electric field)
Question: Draw the Faraday and equipotential diagrams for the following: a) positive point charge b) negative point charge c) opposite point charges d) like point charges e) opposite plate charges. Write the equations that apply to these situations.
Activities:
Positive Charge
Largest potential near charge
Potential at infinity defined to be zero
Negative Charge
Smallest potential near charge
Potential at infinity = -infinity
Opposite Charges
Potential decreases as move away from + charge
Potential largest between charges