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 = -W
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

5. Preflight 3.2
motion C - 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. Preflight 3.3 C 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.

7. ACT: Work C
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

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)?
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? 3
A) W = mJ
B) W = 0 mJ
C) W = mJ
5 m
5 m 1 2
5 m

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

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

14. 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”

15. Preflight 3.7 The electric potential at point A is _______ at point B
greater than
equal to
less than

16. 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

17. 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 +

18. 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

19. 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

20. ACT: Electric Potential+ C B A
The electric potential at A is ___________ the electric potential at B.
greater than
equal to
less than

21. 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!

22. 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?

23. 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)