Electric field, field of multiple charges, field of continuous charge, parallel plate capacitor, motion of charge in electric field, motion of dipole in field

1. General Physics
Physics 120
Chapter 27: THE ELECTRIC
FIELD
Antelope Valley College
Math & Sciences Dept
George Cross

2. TODAYS LECTURE
• THE ELECTRIC FIELD
– Electric Field Models
– The Electric Field of Multiple Point Charges
– The Electric Field of a Continuous Charge
Distribution
– The Electric Fields of Rings, Disks, Planes,
and Spheres
– The Parallel-Plate Capacitor
– Motion of a Charged Particle in an Electric
Field
– Motion of a Dipole in an Electric Field

3. CHAPTER 27 QUIZ
1. Which statement/s is/are not true?
• The electric field obeys the principle of superposition.
• The tangent to an electric field line at a point gives the
direction of the field at that point.
• The density of electric field lines is directly proportional to
the strength of the field.
• Negative charges are sources of electric field lines and
positive charges are sinks of electric field lines.
• Electric fields are what you find in PlayStation football
and soccer games.

4. CHAPTER 27 QUIZ
2. An electric dipole in a uniform electric field
experiences
• Happiness and excitement
• only a net external force.
• only a torque.
• both a net external force and a torque.
• neither a net external force nor a torque.
• answer depends on the strength of the field

5. 3. Choose the correct statement/s
concerning electric field lines:
a.) field lines may cross
b). field lines are close together where the field
is large
c). field lines point away from negative charge
d). a point charge released from rest moves
along a field line
e). field lines are made with white chalk
f). none of these are correct

6. 4. What device provides a practical way to
produce a uniform electric field?
a). A Cathodic Ray Tube
b). An Infinite line of charge
c). An infinite sheet of charge
d). A parallel plate capacitor
e). X-Box
f). A battery

7. 5. Which of these charge distributions did
not have its electric field calculated in
detail in Chapter 27?
a. A line of charge.
.
b. A ring of charge.
.
c. A plane of charge
d. A parallel-plate capacitor
e. They were all calculated

8. CHAPTER 27 QUIZ
1. Which statement/s is/are not true?
• The electric field obeys the principle of superposition.
• The tangent to an electric field line at a point gives the
direction of the field at that point.
• The density of electric field lines is directly proportional to
the strength of the field.
• Negative charges are sources of electric field lines and
positive charges are sinks of electric field lines.
• Electric fields are what you find in PlayStation football
and soccer games.

9. CHAPTER 27 QUIZ
2. An electric dipole in a uniform electric field
experiences
• Happiness and excitement
• only a net external force.
• only a torque.
• both a net external force and a torque.
• neither a net external force nor a torque.
• answer depends on the strength of the field

10. 3. Choose the correct statement/s
concerning electric field lines:
a.) field lines may cross
b). field lines are close together where the field
is large
c). field lines point away from negative charge
d). a point charge released from rest moves
along a field line
e). field lines are made with white chalk
f). none of these are correct

11. 4. What device provides a practical way to
produce a uniform electric field?
a). A Cathodic Ray Tube
b). An Infinite line of charge
c). An infinite sheet of charge
d). A parallel plate capacitor
e). X-Box
f). A battery

12. 5. Which of these charge distributions did
not have its electric field calculated in
detail in Chapter 27?
a. A line of charge.
.
b. A ring of charge.
.
c. A plane of charge
d. A parallel-plate capacitor
e. They were all calculated

13. Electric Field Models
We can understand
much of
electrostatic and
electrodynamic
physics using 4
simple field
models

14. Electric Field of a Point Charge
For multiple charges:
Fon q = F1on q + F2on q + F3on q + …
Enet = Fon q/q = F1onq/q + F2on q/q + F3on q/q + …
Enet = ΣEi (Principle of Superposition)

15. Simple Example of Superposition Principle

16. Limiting Cases & Typical Field Strengths
•
•
•
Near an object, electric field depends on object shape and charge
distribution
Far away from the object, it appears to be a point charge
These are limiting cases. We will use limiting cases to help us
understand and simplify our discussion during class

17. Example of strong
electric field:
ionizes the gas
inside the field

18. The Electric Field of Multiple Point
Charges
• Superposition Principle allows us to sum
electric fields from all charges
• Often easier to break them into components
and sum them for each unit vector, i,j,k
• See Problem Solving Strategy on p. 820 &
example on p. 821

19. Determining Electric Field

20. Determining Electric Field

21. The Electric Field of a Dipole
• An electric dipole is two equal but opposite
charges separated by a small distance s

22. The Electric Field of a Dipole
•An electric dipole is two equal but
opposite charges separated by a
small distance
•May be permanent or induced
•Has zero net charge
•Has an electric field

23. This is true for any
point along the
X-axis.

24. Dipole Moment
Units of dipole moment are Cm

25. The Electric Field of a Dipole
• An electric dipole is two equal but opposite
charges separated by a small distance s
• Dipole moment p = qs

26. The Electric Field of a Dipole
• An electric dipole is two equal but opposite
charges separated by a small distance s
• Dipole moment p = qs
Are we violating
Coulombs Law by
Having an r3 in the
Equation?
• Field
of a dipole drops off with distance much
more quickly than a point charge
(Why? It is electrically neutral.) Coulomb’s
Law deals with point charges, not dipoles.

27. Field Lines and Field Vectors
Another way to
visualize an electric
field is to draw field
lines instead of field
vectors like we did in
Chapter 26.
For a point charge,
the field lines were
straight in to the
center or straight
out from the center.
For a dipole field
lines are curved.

28. Electric Field Lines
• Continuous curves drawn tangent to field vectors,
therefore, field vector is tangent to field line
• Spacing indicates field strength
– Closely spaced – strong field
– Widely spaced – weak field
• Electric field lines never cross
• Electric field lines start from positive charges and end
on negative charges
• Draw arrows along field lines to indicate direction
• Just because there is no field line drawn at a specific
point doesn’t mean that there is no field there. This is
only a way to represent field

29. Using a Test Charge to Determine the
Direction of the Force Due to the Dipole
Electric Field
Field lines follow the direction
of the force measured (or
equivalently – the electric
field vectors).

30. Visualizing the Electric Field of a Dipole
Force is parallel
to field vectors

31. Using a Test Charge to Determine
the Direction of the Force Due to
Multiple Charges

32. Electric Field of a Continuous Charge
• We will view a collection of atoms making up
an extended 3-D object as continuous matter.
This discussion will be based upon this view.
• Any charged metal object will, since it is a
conductor, be uniformly charged over its entire
surface – we will consider this to be
continuous charge (we will assume it is
uniformly charged unless specified otherwise)
• Use Q for the total charge on the metal object

33. Linear Charge Density
Linear charge
density units are
C/m

34. Surface Charge Density
Surface charge density
units are C/m2

35. Finding Electric Field of a Line Charge

36. Finding Electric Field of a Line Charge
Check out Problem Solving Strategy on page 826

37. Electric Field of an Infinite Line of Charge
• Decreases more slowly than for a point charge
(1/r)
• This will be approximately true for any r<<L
– The field is defined by the closest charges to the
point of interest
– Outlying points too far away to have much effect
• Realistic finite line charges can be
approximated using the equation above

38. Electric Field For an Infinite Line of Charge

40. Electric Field For a Ring of Charge

41. Electric Field For a Ring of Charge

43. Electric Field For a Disk of Charge

44. Electric Field For a Plane of Charge

45. Electric Field For a Plane of Charge

47. Electric Field For a Sphere of Charge

49. The Parallel Plate Capacitor

50. The Parallel Plate Capacitor

53. Motion of a Charged Particle in an
Electric Field
• Established forces on a charge in an electric
field
• Net force means acceleration (motion)
• F = ma = mv2/r = qE
• a = qE/m = constant if field is uniform
• Motion in a non-uniform field can be very
complicated
• One simple example of motion in a nonuniform field is orbital motion such as a
negatively charged particle around a positive
charge

54. Motion of a Charged Particle in an
Electric Field

55. Circular Motion of a Charge
F = |q|E = mv2/r

56. Motion of a Dipole in an Electric Field

57. A Sample of Permanent Dipoles Align
to the Electric Field

58. Motion of a Dipole in an Electric Field

59. Examples of
Dipoles in a
Non-Uniform
Field
Dipoles in a non-uniform electric
field will experience a net force.

60. Backup Slides