1. Physics 102: Lecture 3 Electric Potential Energy & Electric Potential

2. Overview for Today’s Lecture
Electric Potential Energy & Work
Uniform fields
Point charges
Electric Potential (like height)
Show large and small battery 9 volt small, 6 volt large

3. Recall Work from Phys 101 Work done by the force given by:
W = F d cos(q)
Positive: Force is in direction moved
Negative: Force is opposite direction moved
Zero: Force is perpendicular to direction moved
Careful ask WHAT is doing work!
Opposite sign for work done by you!
Conservative Forces
D Potential Energy = -Wforce
Use book or brick for prop. Ask students if I am doing positive or negative work, what about gravity.

4. Preflight 3.1 !!!!ACT!!!! Uniform EB –
Uniform E
In what direction does the force on a negative charge at point A point?
left
right up
55%
43% 2%
Electric field points in the direction a POSITIVE charge would feel force.

5. Preflight 3.2
motion C
“I would say zero because the path is perpendicular to the field” - F A B
Uniform E
When a negative charge is moved from A to C the ELECTRIC force does
positive work.
zero work.
negative work. 8%
88% 4%

6. Preflight 3.3 C
“because the direction of the displacement is 180 degrees from direction of the force ” A B - F
Uniform E
motion
When a negative charge is moved from A to B the ELECTRIC force does
positive work.
zero work.
negative work.
66% 5%
29%
ΔUE = -WE field = +WYou
Electric force did negative work
You did positive work
Electric potential energy increased

7. ACT: Work Uniform E Path does not matter! Only end points matter
WA-B = work done by FE moving charge from A to B A B - F
Uniform E
The negative charge is moved from A to C to B. Is the work done by the electric force:
A) Greater than WA-B
B) Same as WA-B
C) Less than WA-B
Work out on slide: W_A-C-B = W_A-C + W_C_B = 0 + Fd_{C-B}cos(theta) = Fd_{A-B} = W_A-B
Path does not matter! Only end points matter

8. Work and D Potential Energy
W = F d cos(q)
Gravity Electric
Brick raised yi yf
Charge moved xi xf
FE = qE (left)
WE = –qEd
DUE= +qEd
FG = mg (down)
WG = –mgh
DUG= +mgh
yi 
yf  h xi  xf  d - F
FG=mg E

9. E.P.E. for point charges Example
E.P.E. of two charges q1 and q2 separated a distance r:
Example
What is the electric potential energy of an electron a distance r = 0.5310-10 m from a proton (H atom)?
UE = (+1.610-19)(-1.610-19)/0.5310-10
= -4.3510-18J
rf = 0.510-10 m + -

10. Work done by YOU to assemble 3 charges
Example
W1 = 0
W2 = k q1 q2 /r
=3.6 mJ
=(9109)(110-6)(210-6)/5
W3 = k q1 q3/r + k q2 q3/r
(9109)(110-6)(310-6)/5 + (9109)(210-6)(310-6)/5 =16.2 mJ
Wtotal = mJ
WE = –19.8 mJ
DUE = mJ
(watch signs!)
Do this live with balls on the table! 3
5 m
5 m 1 2
5 m

11. ACT: Work done by YOU to assemble 3 negative charges
How much work would it take YOU to assemble 3 negative charges?
Likes repel, so YOU will still do positive work! 3
A) W = mJ
B) W = 0 mJ
C) W = mJ
5 m
5 m 1 2
5 m

12. Preflight 3.11 1 +
5 m
5 m + - 2
5 m 3
The total work required by you to assemble this set of charges is:
(1) positive
(2) zero
(3) negative
Bring in (1): zero work
Bring in (2): positive work
Bring in (3): negative work x 2
50%
18%
32%

13. Electric Potential (like height)
Units Joules/Coulomb  Volts
Examples:
Batteries
Outlets
EKG
Only potential differences matter
Comment on lab w/ equipotential lines

14. Electric Potential (like height)
Devil’s Tower
Topographical map
Moving to higher potential  moving uphill

15. Demo: electric potential
Recall electric dipole +
Equipotential lines + – –
Electric field
+ (–) charge has high (low) potential
Equipotential lines at same “height”
Electric field lines point “downhill”

16. Preflight 3.7
Electric field Points from greater potential to lower potential
The electric potential at point A is _______ at point B
greater than
equal to
less than
45%
32%
23%

17. Preflight 3.9
E=0
conductor
The electric potential at point A is _______ at point B
greater than
equal to
less than 7%
85%
“The electric field within a conductor is zero, and therefore, the potential for points A and B are the same”

18. Potential for Point charges
Electric potential a distance r from a charge q:
Example
What is the electric potential a distance r = 0.5310-10 m from a proton? (Let V()=0)
V =UE/q= k q/ r =
(9109)(1.610-19) /0.5310-10
= 27.2 Volts
rf = 0.510-10 m +

19. Example
Two Charges
Calculate electric potential at point A due to charges
Calculate V from +7mC charge
Calculate V from –3.5mC charge
Add (EASY! NO VECTORS) A
V = kq/r
V7 = (9109)(710-6)/5 = 12.6103V
V3 = (9109)(-3.510-6)/5 = -6.3103V
Vtotal = V7+V3 = +6.3103V
4 m
6 m
Q=+7.0mC
Q=-3.5 mC
How much work do you have to do to bring a 2 mC charge from far away to point A?
W=DU=Vq
= (+6.3103V)(2mC)
= mJ

20. ACT: Two Charges
In the region II (between the two charges) the electric potential is
1) always positive
2) positive at some points, negative at others.
3) always negative I II
III
Q=+7.0mC
Q=-3.5 mC
Very close to positive charge potential is positive
Very close to negative charge potential is negative

21. ACT: Electric Potential+ C B A
The electric potential at A is ___________ the electric potential at B.
greater than
equal to
less than
1) Electric field lines point “down hill”
2) AC is equipotential path (perpendicular to E)
3) CB is down hill, so B is at a lower potential than (“down hill from”) A

22. Comparison: Electric Potential Energy vs. Electric Potential
Electric Potential Energy (U) - the energy of a charge at some location.
Electric Potential (V) - found for a location only – tells what the EPE would be if a charge were located there (usually talk about potential differences between two locations):
U = Vq
Neither has direction, just value.
Sign matters!

23. Relationship between F, E, UE, V
Vector
Number (“scalar”) F UE
[N]
[J]
interacting charges
Property of
Ex:
Ex: E V
[N/C]=[V/m]
[J/C]=[V]
Property of
point in space
Sometimes is more useful to think in terms of F and E, other times U and V
Ex:
Ex:
Why so many ways to describe electric force?

24. Electron microscope Uniform E Example ΔV=10kV Vi Vf
Electron gun Vi Vf -
Uniform E
motion
What is the final velocity of the e-?
Solve by conservation of energy:
K.E.i + P.E.i = K.E.f + P.E.f
0 + –eVi = ½mv2 + –eVf
Could solve this using F=ma & kinematic equations (Phys 101)
TRY AT HOME! (HARDER)

25. See everyone Monday!