1. Chapter 18: Electrical Energy and Capacitance
Physics
Chapter 18:
Electrical Energy
and Capacitance

2. Electrical Energy and Capacitance
Electric Field
Surrounds All Charged Particles
Electric Force
Applied by an Electric Field

3. Electrical Energy and Capacitance
Electrical Potential Energy (PE)
Electrical Force Can Move Charged Particles
Movement of a Mass Over a Distance is Work
Electrical Force Does Work in the Form of Electrical Potential Energy

4. Electrical Energy and Capacitance
Electrical Potential Energy (PE)
Uniform Electric Field
How about something other than particles?

5. Electrical Energy and Capacitance
Electrical Potential Energy (PE)
Uniform Electric Field
Charged Plates

6. Electrical Energy and Capacitance
Electrical Potential Energy (PE)
Uniform Electric Field
Charged Plates
Direction of E Field

7. Electrical Energy and Capacitance
Electrical Potential Energy (PE)
Uniform Electric Field
Charged Plates
+q0i
E Field

8. Electrical Energy and Capacitance
Electrical Potential Energy (PE)
Uniform Electric Field
Charged Plates
+q0i
Displacement Due to Applied Force
E Field
+q0f

9. Electrical Energy and Capacitance
Electrical Potential Energy (PE)
In the Same Way that Work is done by Gravitational Force…Wg=DPEg
Electric Force does Work as a Force Vector on a Test Charge (q0)

10. Electrical Energy and Capacitance
Electrical Potential Energy (PE)
PE Decreases for a + Charge
PE Increases for a - Charge

11. Electrical Energy and Capacitance
Electrical Potential Energy (PE)
Also Applies to Displacement of Charged particles Due to Other Charged Particles

12. Electrical Energy and Capacitance
Electrical Potential Energy (PE)
Units
Energy, so…
Joules

13. Electrical Energy and Capacitance
Electric Potential Difference (V)
As the Positive Charge Moves from the Positive Plate to the Negative Plate the PE Decreases
At Any Point in the Field, the PE will Increase with Increased Charge
+q0i
+q0f

14. Electrical Energy and Capacitance
Electric Potential Difference (V)
This Potential Difference is Measured in Joules/Coulomb (Energy/Charge)
The Units of Potential Difference are Volts (V)
+q0i
+q0f

15. Electrical Energy and Capacitance
Electric Potential Difference (V)
+q0i
+q0f

16. Electrical Energy and Capacitance
Electric Potential Difference (V)
+q0i
+q0f

17. Electrical Energy and Capacitance
Electric Potential Difference
Problem “PE Difference”
q0 = 3x10-9C
Wa-b = 6x10-8J
What is DEPE?
What is DV?
q0a E
q0b

18. Electrical Energy and Capacitance
Electric Potential Difference
Solution “PE Difference”
q0 = 3x10-9C
Wa-b = 6x10-8J
What is DEPE?
DEPE = -Wa-b = -6x10-8J
q0a E
q0b

19. Electrical Energy and Capacitance
Electric Potential Difference
Solution “PE Difference”
q0 = 3x10-9C
Wa-b = 6x10-8J
What is DV?
q0a E
q0b

20. Electrical Energy and Capacitance
Electric Potential Difference
Note in the Previous Problem
q0 had a Positive Charge
A Positive Charge Moves from Higher PE to Lower PE
A Negative Charge Moves from Lower PE to Higher PE
-q0b
q0a E E
-q0a
q0b

21. Electrical Energy and Capacitance
Electric Potential Difference
Problem “The Light Will Come On”
Electron Particle: q1 = 1.6x10-19C
System Voltage: V = 12 J/C
System Power (Light) = 40 W
Time = 1 minute
How Many Electrons Will Pass, and in Which Direction?
-q0 E
-q0

22. Electrical Energy and Capacitance
Electric Potential Difference
Solution “The Light Will Burn”
Electron Particle: q1 = 1.6x10-19C
System Voltage: V = 12 J/C
System Power (Light) = 40 W
Time = 1 minute
Energy = Power x Time
DEPE = 40W x 60s = 2400 w/s (J)
q0 = DEPE/DV = 2400J/12V = 2x102C
-q0 E
-q0

23. Electrical Energy and Capacitance
Electric Potential Difference
Solution “The Light Will Burn”
q0 = DEPE/DV = 2400J/12V = 2x102C
Total Particles:
q0 / q (-e) = (2x102C) / (1.6x10-19C)
= 1.3x1021
Direction?
“A Negative Charge Moves from Lower PE to Higher PE”
-q0b E
-q0a

24. Electrical Energy and Capacitance
Electric Potential Difference
Energy, The Big Picture
Translational KE
Rotational KE
Gravitational PE
Elastic PE
Electric PE

25. Electrical Energy and Capacitance
Electric Potential Difference
Problem: “Energy Conserved?”
Particle Moves from Point “a” to Point “b” by Electric Force
Mass = 3.6x10-3kg
Charge (q0) = 6x10-3C
DV = 25V
V0 = 0
What is the Particle Speed at Point “b”? + - a b

26. Electrical Energy and Capacitance
Electric Potential Difference
Solution: “Energy Conserved?”
Mass = 3.6x10-3kg
Charge (q0) = 6x10-3C
DV = 25V
V0 = 0
Rotation = 0
Elasticity = 0
Enet = Translational KE + Gravitational PE + EPE

27. Electrical Energy and Capacitance
Electric Potential Difference
Solution: “Energy Conserved?”
Mass = 3.6x10-3kg
Charge (q0) = 6x10-3C
DV = 25V
V0 = 0
ha = hb (Horizontal Movement Only)
EPEa – EPEb = q0(va-vb)
So…

28. Electrical Energy and Capacitance
Electric Potential Difference
Solution: “Energy Conserved?”
Mass = 3.6x10-3kg
Charge (q0) = 6x10-3C
DV = 25V
V0 = 0

29. Electrical Energy and Capacitance
Electric Potential Difference
Solution: “Energy Conserved?”
Mass = 3.6x10-3kg
Charge (q0) = 6x10-3C
DV = 25V
V0 = 0

30. Electrical Energy and Capacitance
Homework
Pages
Problems:
12 (2.6x104V)
13 (-154V)
32 (4000V/m)

31. Electrical Energy and Capacitance
Capacitors
Two Conductors Placed Near Each Other but Not Touching
The Area Between the Conductors is Filled With an Insulating Material (Dielectric)

32. Electrical Energy and Capacitance
Capacitors
Dielectric
Contains Dipolar Molecules
+ Charge on One End
Charge on the Other End E
Dielectric
Material -

33. Electrical Energy and Capacitance
Capacitors
Dielectric
Each Molecule Accepts Charge (q) E
Dielectric
Material - - + - +

34. Electrical Energy and Capacitance
Capacitors
Dielectric
Each Molecule Accepts Charge (q)
Entire Dielectric Material Becomes Charged E
Dielectric
Material - - +

35. Electrical Energy and Capacitance
Capacitors
Store Electric Charge
Positive and Negative Terminals Carry the Same Charge Magnitude

36. Electrical Energy and Capacitance
Capacitors
Capacitance (C)
The Ability of the Capacitor to Store Charge E
Dielectric
Material -

37. Electrical Energy and Capacitance
Capacitors
Units
coulomb/volt
Farad
(after Michael Faraday) E
Dielectric
Material -

38. Electrical Energy and Capacitance
Varies with Type, Size, and Shape
Parallel Plate
Permittivity of Free Space
8.85x10-12C2/Nm2 E
Dielectric
Material -

39. Electrical Energy and Capacitance
Capacitors
Due to the Charged Molecules of the Dielectric, the Electric Field (E) is Reduced E
Dielectric
Material - - +

40. Electrical Energy and Capacitance
Capacitors and Electric PE
Stored Charge is Stored Electric Potential Energy E
Dielectric
Material - - +

41. Electrical Energy and Capacitance
Capacitors and Electric PE
Stored Charge is Stored Electric Potential Energy

42. Electrical Energy and Capacitance
Homework
Pages
Problems:
26 (7.2x10-11C)
27 (a, 1.3x10-3C b, 4.2J)
43 (4x10-6F)