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

3. 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 07

4. Recall Work from P101 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 = -W
Use book or brick for prop. Ask students if I am doing positive or negative work, what about gravity. 09

5. Preflight 3.1 !!!!ACT!!!! Uniform E
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Frequency to “BB” C
Preflight 3.1
!!!!ACT!!!! F A B -
Uniform E
In what direction does the force on a negative charge at point A point?
left
right up
51%
48% 1%
Electric field points in the direction a POSITIVE charge would feel force. 10

6. Preflight 3.2
motion - F C - F
“I would say zero because the path is perpendicular to the field” - F - F - 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. 6%
89% 5% 11

7. Preflight 3.3 C
“because the direction of the displacement is 180 degrees from direction of the force ” A B - F - F - F - F - F -
Uniform E
motion
When a negative charge is moved from A to B the ELECTRIC force does
positive work.
zero work.
negative work.
67% 4%
29% 13

8. Preflight 3.5 C A B - - - - -
Uniform E
When a negative charge is moved from A to B, the electric potential energy of the charge
Increases
is constant
decreases
36%
14%
49%
E.P.E. = -WE field
Electric force did negative work so electric potential energy increased. 14

9. ACT: Electric Potential Energy
AC: W=0 E + C
CB: W<0 B A - - - - -
When a negative charge is moved from A to B, the electric potential energy of the charge
(A) increases
(B) is constant
(C) decreases
Now switch to point charges!
1) The electric force is directed to bring the electron closer to the proton.
2) Since the electron ends up further from the proton the electric field did negative work.
3) So the electric potential energy increased 17

10. Work and D Potential Energy
W = F d cos(q)
Gravity Electric
Brick raised yi yf
Charge moved ∞  rf
FE = kq1q2/rf2 (left)
WE = -kq1q2/rf
DUE= +kq1q2/rf
FG = mg (down)
WG = -mgh
DUG= +mgh
yf
Fg=mg
Fg=mg rf
Fg=mg h
Fg=mg
Fg=mg
Fg=mg
Fg=mg
yi
Fg=mg 20

11. 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 = mJ
DUE = mJ
(watch signs!)
Do this live with balls on the table! 3
5 m
5 m 1 2
5 m 24

12. 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
W = mJ
W = 0 mJ
W = mJ
5 m
5 m 1 2
5 m 27

13. 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
55%
18%
27%

14. Electric Potential (like height)*
Devil’s Tower
Topographical map
Moving to higher potential  moving uphill 30

15. Demo: electric potential
– charge
+ charge
Equipotential lines

16. Electric Potential (like height)*
Units Joules/Coulomb Volts
Batteries
Outlets
EKG
Really Potential differences
Equipotential lines at same height
Field lines point down hill
V = k q/r (distance r from charge q)
V(∞) = 0
Comment on lab w/ equipotential lines 31

17. 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
51%
25%
24% 32

18. Preflight 3.9 The electric potential at point A is _______ at point B
conductor
The electric potential at point A is _______ at point B
greater than
equal to
less than
“The electric field within a conductor is zero, and therefore, the potential for points A and B are the same 33

19. Preflight Summary Path Vfinal - Vinitial Charge WE field D U = q DV +
Negative
A→ B
Positive
Negative
Positive
Negative
A → C + -
Zero
C → B
Negative + - 35

20. 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 38

21. Electric Potential due to Proton
Example
Electric Potential due to Proton
What is the electric potential a distance r= 0.5310-10 m from a proton? (Let V()=0)
V =U/q= k q/ r =
(9109)(1.610-19) /0.5310-10
= 27.2 Volts
rf = 0.510-10 m + 42

22. Electric Potential due to Proton
What is the electric potential a distance r= 0.5310-10 m from a proton? (Let V()=0)
V =U/q= k q/ r = (9109)(1.610-19) /0.5310-10= 27.2 Volts
What is the electric potential energy of an electron a distance r= 0.5310-10 m from a proton?
U = Vq = (27.2)(-1.610-19)
= -4.3510-18J
Hydrogen Balloon E≈ (4.3510-18)(610+23J )=106 J!
rf = 0.510-10 m + - 42

23. 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!

25. 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!)
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 A
4 m
6 m
Q=+7.0mC
Q=-3.5 mC
W=DU=DVq
=(+6.3103V)(2mC)
=+12.6 mJ
How much work do you have to do to bring a 2 mC charge from far away to point A? 46

26. 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 48

27. To Do Bring “Problem Solver” to discussion section Complete preflight50