1. Chapter 21 Electric Charge and Electric Fields
What is a field?
Why have them?
What causes fields?
Field Type
Caused By
gravity
mass
electric
charge
magnetic
moving charge

2. Electric Charge Types: Arbitrary choice
Positive
Glass rubbed with silk
Missing electrons
Negative
Rubber/Plastic rubbed with fur
Extra electrons
Arbitrary choice
convention attributed to ?
Units: amount of charge is measured in [Coulombs]
Empirical Observations:
Like charges repel
Unlike charges attract

4. Charge in the Atom
Protons (+)
Electrons (-)
Ions
Polar Molecules

5. Charge Properties Conservation Quantization
Charge is not created or destroyed, only transferred.
The net amount of electric charge produced in any process is zero.
Quantization
The smallest unit of charge is that on an electron or proton. (e = 1.6 x C)
It is impossible to have less charge than this
It is possible to have integer multiples of this charge

6. Conductors and Insulators
Conductor transfers charge on contact
Insulator does not transfer charge on contact
Semiconductor might transfer charge on contact

7. Charge Transfer Processes
Conduction
Polarization
Induction

8. The Electroscope

9. Coulomb’s Law Empirical Observations Formal Statement
Direction of the force is along the line joining the two charges

10. Active Figure 23.7
(SLIDESHOW MODE ONLY)

11. Coulomb’s Law Example
What is the magnitude of the electric force of attraction between an iron nucleus (q=+26e) and its innermost electron if the distance between them is 1.5 x m
3.The magnitude of the Coulomb force is
F = kQ1Q2/r2
= (9.0 ´ 109 N · m2/C2)(26)(1.60 ´ 10–19 C)(1.60 ´ 10–19 C)/(1.5 ´ 10–12 m)2
= ´ 10–3 N.

12. Hydrogen Atom Example
The electrical force between the electron and proton is found from Coulomb’s law
Fe = keq1q2 / r2 = 8.2 x 108 N
This can be compared to the gravitational force between the electron and the proton
Fg = Gmemp / r2 = 3.6 x N

13. Subscript Convention
+q1
+q2

14. More Coulomb’s Law +q1 +q2 Coulomb’s constant:
permittivity of free space:
Charge polarity: Same sign Force is right
Opposite sign Force is Left
Electrostatics --- Charges must be at rest!

15. Superposition of Forces
+Q1
+Q2
+Q0
+Q3

16. Coulomb’s Law Example Q = 6.0 mC L = 0.10 m
What is the magnitude and direction of the net force on one of the charges?
We find the magnitudes of the individual forces on the
charge at the upper right corner:
F1= F2 = kQQ/L2 = kQ2/L2
= (9.0 ´ 109 N · m2/C2)(6.00 ´ 10–3 C)2/(0.100 m)2
= 3.24 ´ 107 N.
F3= kQQ/(L√2)2 = kQ2/2L2
= (9.0 ´ 109 N · m2/C2)(6.00 ´ 10–3 C)2/2(0.100 m)2
= 1.62 ´ 107 N.
The directions of the forces are determined from the signs
of the charges and are indicated on the diagram. For the
forces on the upper-right charge, we see that the net force
will be along the diagonal. For the net force, we have
F = F1 cos 45° + F2 cos 45° + F3
= 2(3.24 ´ 107 N) cos 45° ´ 107 N
= 6.20 ´ 107 N along the diagonal, or away from the center of the square.
From the symmetry, each of the other forces will have the same magnitude and a direction away from the center: The net force on each charge is ´ 107 N away from the center of the square.
Note that the sum for the three charges is zero.

17. Zero Resultant Force, Example
q1 = 15.0 mC
Where is the resultant force equal to zero?
The magnitudes of the individual forces will be equal
Directions will be opposite
Will result in a quadratic
Choose the root that gives the forces in opposite directions
q2 = 6.0 mC

18. Electrical Force with Other Forces, Example
The spheres are in equilibrium
Since they are separated, they exert a repulsive force on each other
Charges are like charges
Proceed as usual with equilibrium problems, noting one force is an electrical force

19. Electrical Force with Other Forces, Example cont.
The free body diagram includes the components of the tension, the electrical force, and the weight
Solve for |q|
You cannot determine the sign of q, only that they both have same sign

20. The Electric Field
Charge particles create forces on each other without ever coming into contact.
“action at a distance”
A charge creates in space the ability to exert a force on a second very small charge. This ability exists even if the second charge is not present.
We call this ability to exert a force at a distance a “field”
In general, a field is defined:
The Electric Field is then:
Why in the limit?

21. Electric Field near a Point Charge+Q -Q
Electric Field Vectors
Electric Field Lines

22. Active Figure 23.13
(SLIDESHOW MODE ONLY)

23. Rules for Drawing Field Lines
The electric field, , is tangent to the field lines.
The number of lines leaving/entering a charge is proportional to the charge.
The number of lines passing through a unit area normal to the lines is proportional to the strength of the field in that region.
Field lines must begin on positive charges (or from infinity) and end on negative charges (or at infinity). The test charge is positive by convention.
No two field lines can cross.

24. Electric Field Lines, General
The density of lines through surface A is greater than through surface B
The magnitude of the electric field is greater on surface A than B
The lines at different locations point in different directions
This indicates the field is non-uniform

25. Example Field Lines Line Charge Dipole
For a continuous linear charge distribution,
Linear Charge Density:

26. Active Figure 23.24
(SLIDESHOW MODE ONLY)

27. More Field Lines
Surface Charge Density:
Volume Charge Density:

28. Superposition of Fields
+q1
+q2 P
+q3

29. Superposition Example
Find the electric field due to q1, E1
Find the electric field due to q2, E2
E = E1 + E2
Remember, the fields add as vectors
The direction of the individual fields is the direction of the force on a positive test charge

30. Electric Field of a Dipoley -q +q

31. Example Three point charges are arranged as shown in Figure P23.19.
Find the vector electric field that the 6.00-nC and –3.00-nC charges together create at the origin.
(b) Find the vector force on the 5.00-nC charge.
Figure P23.19

32. Example
Three point charges are aligned along the x axis as shown in Figure P Find the electric field at
the position (2.00, 0) and
the position (0, 2.00).
Figure P23.52

33. FIG. P23.52(a)
in +x direction.

34. P23.19
(a)
(b)

35. Motion of Charged Particles in a Uniform Electric Field-Q +Q

36. Example
A proton accelerates from rest in a uniform electric field of 500 N/C. At some time later, its speed is 2.50 x 106 m/s.
Find the acceleration of the proton.
How long does it take for the proton to reach this speed?
How far has it moved in this time?
What is the kinetic energy? e -Q +Q

37. Motion of Charged Particles in a Uniform Electric Field+Q -e -Q

38. Active Figure 23.26
(SLIDESHOW MODE ONLY)

39. Motion of Charged Particles in a Uniform Electric Field-Q +Q
Phosphor
Screen
This device is known as a
cathode ray tube (CRT)

40. Dipoles
The combination of two equal charges of opposite sign, +q and –q, separated by a distance l -q +q

41. Dipoles in a Uniform Electric Field+q -q

42. Work Rotating a Dipole in an Uniform Electric Field+q -q