1. Electric Potential Energy
The electric potential energy of charge q in a uniform electric field is
where s is measured from the negative plate and U0 is the potential energy at the negative plate (s = 0). It will often be convenient to choose U0 = 0, but the choice has no physical consequences because it doesn’t affect ΔUelec, the change in the electric potential energy. Only the change is significant.

2. Analogy to Gravitational PE
Gravitation PE depends on mass
Electric potential energy depends
on charge
General Physics 2
Electric Potential

4. The Potential Energy of Point Charges
Consider two point charges, q1 and q2, separated by a distance r. The electric potential energy is
This is explicitly the energy of the system, not the energy of just q1 or q2.
Note that the potential energy of two charged particles approaches zero as r  .

6. Which set has a positive potential energy?
PE =0 at infinity
did you do work to assemble the charges from infinity?
yes -> PE > no -> PE < 0

7. Which set has a negative potential energy?
1 and 2
PE =0 at infinity
did you do work to assemble the charges from infinity?
yes -> PE > 0
no -> PE < 0

8. EXAMPLE 29.2 Approaching a charged sphere

9. EXAMPLE 29.2 Approaching a charged sphere

10. The Potential Energy of a Dipole
The potential energy of an electric dipole p in a uniform electric field E is
The potential energy is minimum at ø = 0° where the dipole is aligned with the electric field.
Remember p = qs

11. Electrical Potential Energy
For a charge in a uniform electric field
For point charges

12. Think-Pair-Share
What is the potential energy of this system, taking U = 0 at a great distance?
V is scalar, so they just add
+4Q
General Physics 2
Electric Potential

13. Workbook Problems on Electric Potential Energy
V is scalar, so they just add
General Physics 2
Electric Potential

14. The Electric Potential
We define the electric potential V (or, for brevity, just the potential) as
Charge q is used as a probe to determine the electric potential, but the value of V is independent of q. The electric potential, like the electric field, is a property of the source charges.
The unit of electric potential is the joule per coulomb, which is called the volt V:

15. The Electric Potential of a Point Charge
Let q be the source charge, and let a second charge q', a distance r away, probe the electric potential of q. The potential energy of the two point charges is
By definition, the electric potential of charge q is
The potential extends through all of space, showing the influence of charge q, but it weakens with distance as 1/r. This expression for V assumes that we have chosen V = 0 to be at r = .

17. connect points in space at same potential
Equipotential Lines
connect points in space at same potential
equipotential surface is perpendicular to electric field lines
General Physics 2
Electric Potential

18. Electric Field & Equipotential Lines
Draw field lines and equipotential lines for the following charge distributions -
General Physics 2
Electric Potential

19. Electric Field & Equipotential Lines
Draw field lines and equipotential lines for the following charge distributions +
General Physics 2
Electric Potential

20. EXAMPLE 29.8 Calculating the potential of a point charge
QUESTIONS:

21. EXAMPLE 29.8 Calculating the potential of a point charge

22. Plug & Chug
What is the electric potential 15.0 cm from a 4.00 x 10-6 C point charge?
General Physics 2
Electric Potential

23. The Electric Potential of a Charged Sphere
In practice, you are more likely to work with a charged sphere, of radius R and total charge Q, than with a point charge. Outside a uniformly charged sphere, the electric potential is identical to that of a point charge Q at the center. That is,
Or, in a more useful form, the potential outside a sphere that is charged to potential V0 is

24. Plug & Chug
What is the electric potential 15.0 cm from a charged sphere with a charge of 4.00 x 10-6 C and a radius of 1.0 cm?
What is the electric potential 20.0 cm from a 1.0 cm diameter charged sphere that has been charged to 1000V?
General Physics 2
Electric Potential

25. The Electric Potential of Many Charges
The electric potential V at a point in space is the sum of the potentials due to each charge:
where ri is the distance from charge qi to the point in space where the potential is being calculated.
In other words, the electric potential, like the electric field, obeys the principle of superposition.

26. EXAMPLE 29.10 The potential of two charges
QUESTION:

27. EXAMPLE 29.10 The potential of two charges

28. The Electric Potential Inside a Parallel-Plate Capacitor
The electric potential inside a parallel-plate capacitor is
where s is the distance from the negative electrode.
The electric potential, like the electric field, exists at all points inside the capacitor.
The electric potential is created by the source charges on the capacitor plates and exists whether or not charge q is inside the capacitor.

29. Electric Potential Think of analogy with gravitational PE, where
object with positive PE will
fall if released.
Here, p+ has high PE
when near + plate and will
“fall” toward negative plate
when released
+ charges
move from
high to low
potential
sense of potential depends on charge!
Think of + charge when
wondering if something is
high or low potential

30. Electric Potential low PE High PE - - Unlike mass, charge can
be + or -. Thus, PE depends
on the sign of the charge.
For example, an e- will have
high PE when near the
plate and will “fall” toward
the + plate when released
- charges
move from
low to high
potential
sense of potential depends on charge!

31. EXAMPLE 29.7 A proton in a capacitor
QUESTIONS:

32. EXAMPLE 29.7 A proton in a capacitor

33. EXAMPLE 29.7 A proton in a capacitor

34. EXAMPLE 29.7 A proton in a capacitor

35. EXAMPLE 29.7 A proton in a capacitor

36. EXAMPLE 29.7 A proton in a capacitor

37. Electrostatic Potential & PE
When dealing with discrete point charges:
U and V are scalars
F and E are vectors
General Physics 2
Electric Potential

38. Workbook P29-6 #11, 13 P29-7 #15 P29-9 #17, 18 P29-10 #20 P29-11 #22
V is scalar, so they just add
General Physics 2
Electric Potential