1. Electrical Energy and Capacitance
Chapter 18
Electrical Energy
and
Capacitance
(But we don’t have to cover capacitance)

2. 18.1 Electrical Potential Energy
Objectives
1. Define electrical potential energy
2. Compare the electrical potential energy for various charge distributions (these charges distributions are uniform and non-uniform electric fields)

3. A Look Back at Gravitational Potential Energy
PEgrav =
mgh
PEgrav=mgh h
PEgrav=0

4. Electric Potential Energy
Potential associated with a charge due to its position relative to a source of electric force
Non-uniform E-field
Uniform E-field

5. Consider: Uniform Electric Field

6. Charge Movement in E Field vs PEelectric
If the charge is moving….
+ Charge
- Charge
With E
Loses PEelectric
Gains PE electric
Opposite E
Gains PEelectric

7. Electrical Potential Energy
(in a uniform field)
ΔPEelectric = -qE(Δd)
q = charge (C)
E = electric field strength (N/C)
Δd = displacement (m) from the
reference point in the
direction of the field
If we assume PEi=0 at di=0, then this equation can
also be written as PEe = -qEd

8. PEe for Uniform E-field
A charge of 7.5μC moves a distance of 0.25m
through a uniform electric field with magnitude
5.50x106 V/m. How much did the charge’s
potential energy change in that distance?
ANS: 10.3J
An electron moves a distance of 0.035m through a
uniform electric field between two oppositely
charged parallel plates. In that span, the electron’s
potential energy changed by 5.60x10-15J. What is the
magnitude of the E-field, and what direction did the
electron move (toward the + plate or – plate)?
ANS: 9.99x105 V/m, moved toward - plate

9. Electrical Potential Energy Associated with a Point Charge
…because point charges produce
non-uniform electric fields

10. Regarding PEelectric for point charges…
The reference point for electrical potential
energy is assumed to be at infinity. Note
that PEelec goes to zero as r goes to infinity.
Because like charges repel, positive work must
be done to bring them together. So, PEelec
is positive for like charges and negative for
unlike charges.
For determining PEelec for more than two
charges, calculate PEelec for each pair then
add the energies.

11. PEe for Non-Uniform E-field
In one model of the hydrogen atom, an electron
in its lowest energy state moves in a circular
orbit about the nucleus (a single proton) at a
distance of 5.29x10-11m. Find the electrical
potential energy of the hydrogen atom.
Answer: PEe = -4.35x10-18 J

12. PEe for More than Two Point Charges
A point charge of 3.0nC is located at the origin.
Another charge of 6.0nC is located at (0.0, 30.0)cm.
What is the electrical potential energy of the
system if a third charge of 4.0nC is at (0.0, 60.0)cm?
b) What is the third charge is at (0.0, -60.0)cm?
c) What is the third charge is -6.0nC and is located at
(0.0, -60.0)cm?
ANS: a) 1.44x10-6J b) 9.6x10-7J c) -8.99x10-8J

13. 18.2 Potential Difference Objectives
Distinguish between electrical potential
energy, electric potential, and potential
difference.
Compute the potential difference for
for various charge distributions (i.e.,
uniform and non-uniform electric fields).

14. Electric Potential (V)
…is the electrical potential energy
associated with a charged particle
divided by the charge of the particle

15. Potential Difference (ΔV)
…is the change in electrical potential energy associated with a charged particle divided by the charge of the particle.

16. What’s another name for PE?
Hint:What do we have to do to a charged
particle if we want to increase it’s PEelec?
PE aka “Work” (W)
units for PE and for work = joules (J)

17. More About Potential Difference
Potential difference is often referred to as “voltage”.
As a 1C charge moved through a potential difference of 1V, the charge gains (or loses) 1J of energy.
Common potential differences (voltages) are 12V for a car battery and 120V between the two slots in a household electrical outlet.

18. Potential Difference in a Uniform Electric Field
We know
V =
And ΔPEelectric = -qEΔd (uniform field) So
ΔV = -EΔd
(where Δd is displacement from a reference
point in the direction of the electric field)

19. ...therefore E units must be ??
V = -E d
Notice…..new units for E !!
V units is volts (V)
d is in meters (m)
...therefore E units must be ??

20. ΔV for uniform electric field
A proton is released from rest in a uniform E-field with a magnitude of 8.0x104 V/m. The proton moves 0.50 m as a result. Find:
a) The potential difference between the initial and final positions of the proton.
b) The change in electrical potential energy of the proton as a result of this displacement.
ANS: a) -4.0x104 V b) -6.4x10-15 J

21. Potential Difference at Some Location Near a Point Charge
(compares the potential difference between a point
at infinity and some location near a point charge)

22. ΔV near a point charge
Find the potential difference between a point infinitely far away from and a point 1.0 cm from a proton.
ANS: 1.44x10-7 V

23. Conservation of Energy
When we think about individual charges moving
through uniform or non-uniform electric fields,
we’re going to assume that the total energy of the
charge remains constant (i.e., energy is conserved).
So, we can say…..
MEi = MEf
KEi + PEgi + PEsi + PEei= KEf + PEgf + PEsf + PEef
But in our electrical calculations we
typically are only dealing with PEe, so…
KEi + PEei = KEf + PEef

24. Conservation of ME
A proton is accelerated from rest through a potential
difference of 220V. What is the velocity of the
proton at this point?
ANS: 2.05x105 m/s

25. Water Analogy

26. PEelectric, Electric Potential, and Potential Difference in a Battery
The potential difference between the
positive and negative terminals is
9V, where the electric potential
at the negative terminal is 0V, and
the electric potential at the positive
terminal is 9V.
When hooked to an electrical device,
the charge moves inside the battery
from negative to positive terminal.
The battery does work on the charge
in order to move it from the (-) to the
(+) terminal, so PEelectric increases.

27. More on PEelectric, Electric Potential and Potential Difference