This document provides an overview of the third lecture in Physics 102 on electric potential. The lecture covers electric potential energy and work in uniform electric fields and point charge configurations. It reviews the concept of work from the previous physics course and introduces electric potential, defined similarly to gravitational potential energy. Electric potential is explored for uniform fields and point charges. Example problems are worked through calculating electric potential energy and electric potential for various charge configurations. Key differences between electric potential energy and electric potential are summarized. The lecture concludes by considering the electric potential in a region between two charges.

1. Physics 102: Lecture 3, Slide 1
Physics 102:
Lecture 3
Electric Potential

2. Physics 102: Lecture 3, Slide 2
Overview for Today’s Lecture
• Electric Potential Energy/ Work
– Uniform fields
– Point charges
• Electric Potential (like height)
– Uniform fields
– Point charges

3. Physics 102: Lecture 3, Slide 3
Recall Work from P101
• Work done by the force given by:
– W = F d cos(θ)
– 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
– ∆ Potential Energy = −W

4. Physics 102: Lecture 3, Slide 4

5. Physics 102: Lecture 3, Slide 5
A B
C
Uniform E→
In what direction does the force on a
negative charge at point A point?
1) left
2) right
3) up
Preflight 3.1
!!!!ACT!!!!

6. Physics 102: Lecture 3, Slide 7
A B
C
Uniform E→
When a negative charge is moved from A to
B the ELECTRIC force does
1) positive work.
2) zero work.
3) negative work.
Preflight 3.3
“because the direction of
the displacement is 180
degrees from direction of
the force ”

7. Physics 102: Lecture 3, Slide 8

8. Physics 102: Lecture 3, Slide 9
A B
C
Uniform E→
Preflight 3.5
When a negative charge is moved from A to B,
the electric potential energy of the charge
1) Increases
2) is constant
3) decreases
E.P.E. = −WE field
Electric force did negative
work so electric potential
energy increased.

9. Physics 102: Lecture 3, Slide 10
A
B
+
ACT: Electric Potential Energy
When a negative charge is moved from A to B, the electric
potential energy of the charge
(A)increases
(B) is constant
(C) decreases
Ε C
AC: W=0
CB: W<0

10. Physics 102: Lecture 3, Slide 11
Work and ∆ Potential Energy
• Brick raised yi→ yf • Charge moved ∞ → rf
• FE = kq1q2/r2
(left)
• WE = -kq1q2/rf
• ∆UE= +kq1q2/rf
W = F d cos(θ)
Gravity Electric
Fg=mg
Fg=mg
Fg=mg
Fg=mg
Fg=mg
Fg=mg
Fg=mg
yi→
yf→
Fg=mg
h
• FG = mg (down)
• WG = -mgh
• ∆UG= +mgh
rf

11. Physics 102: Lecture 3, Slide 12

12. Physics 102: Lecture 3, Slide 13
Work done by YOU
to assemble 3 charges
• W1 = 0
1
3
2
5 m
5 m5 m
• W2 = k q1 q2 /r =(9×109
)(1×10-6
)(2×10-6
)/5 =3.6 mJ
• 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 = +19.8 mJ
• WE = -19.8 mJ
• ∆UE = +19.8 mJ
(watch signs!)

13. Physics 102: Lecture 3, Slide 14
ACT: Work done by YOU
to assemble 3 negative charges
1
3
2
5 m
5 m5 mA.W = +19.8 mJ
B.W = 0 mJ
C.W = -19.8 mJ
How much work would it take YOU to assemble 3 negative
charges?
Likes repel, so YOU will still do positive
work!

14. Physics 102: Lecture 3, Slide 15
Preflight 3.11
The total work required by you to assemble
this set of charges is:
(1) positive
(2) zero
(3) negative
+
+
-5 m
5 m5 m
1
32

15. Physics 102: Lecture 3, Slide 16

16. Physics 102: Lecture 3, Slide 17
Electric Potential (like height)*
Mount Tabor
Moving to higher potential  moving uphill

17. Physics 102: Lecture 3, Slide 18
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

18. Physics 102: Lecture 3, Slide 19
Preflight 3.7
The electric potential at point A is _______ at point B
1) greater than
2) equal to
3) less than
Electric field Points from
greater potential to lower
potential

19. Physics 102: Lecture 3, Slide 20

20. Physics 102: Lecture 3, Slide 21
Preflight 3.9
The electric potential at point A is _______ at point B
1) greater than
2) equal to
3) less than
conductor

21. Physics 102: Lecture 3, Slide 22
Preflight Summary
A→ B Negative
C → B
A → C
Zero
Path Vfinal - Vinitial ∆ U = q ∆V WE field
Negative
Charge
+
-
+
-
+
-
Negative
Positive
Positive
Negative

22. Physics 102: Lecture 3, Slide 24

23. Physics 102: Lecture 3, Slide 25
A
B
+
ACT: Electric Potential
The electric potential at A is ___________ the electric
potential at B.
1) greater than
2) equal to
3) less than
C

24. Physics 102: Lecture 3, Slide 26
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 =
+
rf = 0.5×10-10
m
(9×109
)(1.6×10−19
) /0.53×10−10
= 27.2 Volts

25. Physics 102: Lecture 3, Slide 27
Electric Potential due to Proton
What is the electric potential a distance r= 0.53×10-10
m from
a proton? (Let V(∞)=0)
+
rf = 0.5×10-10
m
What is the electric potential energy of an electron a
distance r= 0.53×10-10
m from a proton?
Hydrogen Balloon E≈ (4.35×10-18
)×(6×10+23
J )=106
J!
V =U/q= k q/ r = (9×109
)(1.6×10-19
) /0.53×10-10
= 27.2 Volts
U = Vq = (27.2)(-1.6×10-19
)
−
= −4.35×10−18
J ≡ −27.2 eV

26. Physics 102: Lecture 3, Slide 28

27. Physics 102: Lecture 3, Slide 29
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!

28. Physics 102: Lecture 3, Slide 30
Two Charges
Q=-3.5 µCQ=+7.0µC
A
6 m
4m
How much work do you have to do to bring
a 2 µC charge from far away to point A?
W=∆U=∆Vq
=(+6.3×103
V)(2µC)
=+12.6 mJ
• Calculate electric potential at point A due to charges
– Calculate V from +7µC charge
– Calculate V from –3.5µC charge
– Add (EASY!)
• V = kq/r
V7=(9×109
)(7×10-6
)/5 = 12.6×103
V
V3=(9×109
)(-3.5×10-6
)/5 = -6.3×103
V
Vtotal = V7+V3 = +6.3×103
V

29. Physics 102: Lecture 3, Slide 31
ACT: Two Charges
Q=-3.5 µCQ=+7.0µC
• In the region II (between the two charges) the
electric potential is
Ι ΙΙ ΙΙΙ
1) always positive
2) positive at some points, negative at others.
3) always negative
Very close to positive charge potential is positive
Very close to negative charge potential is negative

30. Physics 102: Lecture 3, Slide 32
To Do
• Bring “Problem Solver” to discussion section
• Complete preflight.