1. Chapter 25 – Electric Potential
What is the value of employing the concept of energy when solving physics problems?
Potential energy can be defined for conservative forces. Is the electrostatic force conservative?
For conservative forces, the work done in moving an object between two points is independent of the path taken. a b

2. Work and Potential Energy for gravity

3. Work and Potential Energy
Electric Field Definition:
Work Energy Theorem a b

4. Electric Potential Differenceb
Definition:

5. What the heck is ds ds

6. What it means:
Potential Difference, Vb-Va is the work per unit charge an external agent must perform to move a test charge from ab without a change in kinetic energy. a b

7. An example

8. Units of Potential Difference
Because of this, potential difference is often referred to as “voltage”
In addition, 1 N/C = 1 V/m - we can interpret the electric field as a measure of the rate of change with position of the electric potential.
So what is an electron Volt (eV)?

9. Electron-Volts
Another unit of energy that is commonly used in atomic and nuclear physics is the electron-volt
One electron-volt is defined as the energy a charge-field system gains or loses when a charge of magnitude e (an electron or a proton) is moved through a potential difference of 1 volt
1 eV = 1.60 x J

10. Example Through what potential difference would one need to
accelerate an electron in order for it to achieve a velocity
of 10% of the velocity of light, starting from rest?
(c = 3 x 108 m/s)

11. Conventions for the potential “zero point”
Choice 1: Va=0
Choice 2:

12. Potential difference for a uniform electric field+Q -Q b d a

13. Potential difference for a point charge+Q

14. ds for a point charge

15. Recall the convention for the potential “zero point”
Equipotential surfaces are concentric spheres

16. Electric Potential of a Point Charge
The electric potential in the plane around a single point charge is shown
The red line shows the 1/r nature of the potential

17. E and V for a Point Charge
The equipotential lines are the dashed blue lines
The electric field lines are the brown lines
The equipotential lines are everywhere perpendicular to the field lines

18. Potential of a charged conductor
Given: Spherical conductor
Charge=Q
Radius=R R
Find: V(r)

19. The plots for a metal sphere

20. Determining the Electric Field from the Potential

21. Superposition of potentials
+Q1
+Q2
+Q3

22. Electric potential due to continuous charge distributions
Single charge
Single piece of a charge distribution +
+Q1
+Q2
+Q3
Discrete charges
Continuous charge distribution

23. Electric Potential for a Continuous Charge Distribution
Consider a small charge element dq
Treat it as a point charge
The potential at some point due to this charge element is

24. Electric field due to continuous charge distributions
Single charge
Single piece of a charge distribution +
+Q3
+Q2
+Q1
Discrete charges
Continuous charge distribution

25. Example: A ring of charge+ + + + + + +

26. Electric field from a ring of charge+ + + + + + +

27. Example: Electric field of a charged ring directly
y-components cancel by symmetry + + + + + + +

28. Potential due to a charged disk

29. Uniformly Charged Disk

30. Electric Dipole

31. Electric Potential of a Dipole
The graph shows the potential (y-axis) of an electric dipole
The steep slope between the charges represents the strong electric field in this region

32. E and V for a Dipole The equipotential lines are the dashed blue lines
The electric field lines are the brown lines
The equipotential lines are everywhere perpendicular to the field lines

33. Potential energy due to multiple point charges
+Q2
+Q1
+Q3
+Q1
+Q2

34. Irregularly Shaped Objects
The charge density is high where the radius of curvature is small
And low where the radius of curvature is large
The electric field is large near the convex points having small radii of curvature and reaches very high values at sharp points

35. Problem P25.23
Show that the amount of work required to assemble four identical point charges of magnitude Q at the corners of a square of side s is 5.41keQ2/s.

36. Example P25.33
An electron starts from rest 3.00 cm from the center of a uniformly charged insulating sphere of radius 2.00 cm and total charge 1.00 nC. What is the speed of the electron when it reaches the surface of the sphere?

37. Example P25.37
The potential in a region between x = 0 and x = 6.00 m is V = a + bx, where a = 10.0 V and b = –7.00 V/m. Determine
the potential at x = 0, 3.00 m, and 6.00 m, and
the magnitude and direction of the electric field at x = 0, 3.00 m, and 6.00 m. At

38. Example 25.43
A rod of length L (Fig. P25.43) lies along the x axis with its left end at the origin. It has a nonuniform charge density λ = αx, where α is a positive constant.
What are the units of α?
Calculate the electric potential at A.
Figure P25.43