1. Electric Charge and Electric Field
Chapter 16
Electric Charge and Electric Field

2. Objectives: The students will be able to:
Apply Coulomb's law to determine the magnitude of the electrical force between point charges separated by a distance r and state whether the force will be one of attraction or repulsion.

3. Two types of charge: Positive Charge: A shortage of electrons.
Negative Charge: An excess of electrons.
Conservation of charge – The net charge of a closed system remains constant.

4. Number of electrons > Number of protons -2e = -3.2 x 10-19C
Nucleus - - + n - n + + n n + n - + + n - - -
Negative Atom
Number of electrons > Number of protons
-2e = -3.2 x 10-19C
Neutral Atom
Number of electrons = Number of protons
Positive Atom
Number of electrons < Number of protons
+2e = +3.2 x 10-19C

5. Inquiry Activity
Electric Field Hockey phET

6. Electric Forces + + - Like Charges - Repel F Unlike Charges - Attract

7. 16.5 Coulomb’s Law
Experiment shows that the electric force between two charges is proportional to the product of the charges and inversely proportional to the distance between them.

8. Coulomb’s Law – Gives the electric force between two point charges.
Inverse Square
Law
k = Coulomb’s Constant = 8.988x109 Nm2/C2
q1 = charge on mass 1
q2 = charge on mass 2
r = the distance between the two charges
The electric force is much stronger than the gravitational force.

9. 16.5 Coulomb’s Law Coulomb’s law:
(16-1)
This equation gives the magnitude of the force.

10. 16.5 Coulomb’s Law
The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if they are the same.

11. 16.5 Coulomb’s Law Unit of charge: coulomb, C
The proportionality constant in Coulomb’s law is then:
Charges produced by rubbing are typically around a microcoulomb:

12. Coulomb's Law
The force between two charges gets stronger as the charges move closer together.
The force also gets stronger if the amount of charge becomes larger.

13. Coulomb's Law
The force between two charges is directed along the line connecting their centers.
Electric forces always occur in pairs according to Newton’s third law, like all forces.

14. Coulomb's Law
The force between charges is directly proportional to the magnitude, or amount, of each charge.
Doubling one charge doubles the force.
Doubling both charges quadruples the force.

15. Coulomb's Law
The force between charges is inversely proportional to the square of the distance between them.
Doubling the distance reduces the force by a factor of 22 = (4), decreasing the force to one-fourth its original value (1/4).
This relationship is called an inverse square law because force and distance follow an inverse square relationship.

16. 16.5 Coulomb’s Law Charge on the electron:
Electric charge is quantized in units of the electron charge.
Unit of charge is a Coulomb (C)

17. Example 1
Two charges are separated by a distance r and have a force F on each other. q1 q2 r F
If r is doubled then F is :
¼ of F
If q1 is doubled then F is : 2F
If q1 and q2 are doubled and r is halved then F is :
16F

18. Example 2
Two 40 gram masses each with a charge of 3μC are placed 50cm apart. Compare the gravitational force between the two masses to the electric force between the two masses. (Ignore the force of the earth on the two masses)
3μC
40g
50cm

19. The electric force is much greater than the gravitational force

20. Homework
Problems page 465
#s 1, 3, 5, 7, 10

21. Objectives: The students will be able to:
Apply Coulomb's law to determine the magnitude of the electrical force between point charges separated by a distance r and state whether the force will be one of attraction or repulsion.

22. Permittivity of free space
For practical reasons, the coulomb is defined using current and magnetism giving
k = x 109 Nm2/C2
Permittivity of free space
Then

23. 16.5 Coulomb’s Law
The proportionality constant k can also be written in terms of , the permittivity of free space:
(16-2)

24. Coulombs Law
Lab Experiment
In 1785 Charles Augustin Coulomb reported in the Royal Academy Memoires using a torsion balance two charged mulberry pithballs repelled each other with a force that is inversely proportional to the distance.
where k=8.99*109 Nm2/C2 in SI unit
k ~ 1010 Nm2/C2 + + q2 q1 r
Repulsion
Point charges + - -
Attraction
Spheres same
as points - -
Repulsion
Summer July 06
PHYS632 E&M

25. Superposition of electric forces
Net force is the vector sum of forces from each charge F3 q1 F q2 F2 q q3 F1
Net force on q: F = F1 + F2 + F3

26. Principle of Superposition Three charges In a line
In the previous example we tacitly assumed that the forces between nuclei simply added and did not interfere with each other. That is the force between two nuclei in each penny is the same as if all the others were not there. This idea is correct and is referred to as the Principle of Superposition.
Example of charges in a line
Three charges lie on the x axis: q1=+25 nC at the origin, q2= -12 nC at x =2m, q3=+18 nC at x=3 m. What is the net force on q1? We simply add the two forces keeping track of their directions. Let a positive force be one in the + x direction. 1 2 x 3

27. Force from many charges- Q2 + Q1 - Q3
Force on charge is vector sum of forces from all charges
Principle of superposition + Q4

28. Example 16-3 p.448
Three charges in a line. Three charged particles
are arranged in a line, as shown below. Calculate the
net electrostatic force on particle 3 (the -4.0μC on the
right) due to the other two charges.

29. Example 16-3 p.448
Three charges in a line. Three charged particles are arranged in a line, as shown below. Calculate the net electrostatic force on particle 3 (the -4.0μC on the
right) due to the other two charges.

30. 16.5 Coulomb’s Law
Coulomb’s law strictly applies only to point charges.
Superposition: for multiple point charges, the forces on each charge from every other charge can be calculated and then added as vectors.

31. 16.6 Solving Problems Involving Coulomb’s Law and Vectors
The net force on a charge is the vector sum of all the forces acting on it.

32. 16.6 Solving Problems Involving Coulomb’s Law and Vectors
Vector addition review:

33. F1 and F2 must be added together as vectors.
Example 3
Three charged objects are placed as shown. Find the net force on the object with the charge of -4μC.
- 5μC
20cm
45º F1
5μC
- 4μC F2
F1 and F2 must be added together as vectors.

34. + F1 = < - 4.5 , 0.0 > F2 = < 1.6 , - 1.6 >
2.3cos45≈1.6
- 2.9 F2
45º
29º θ
- 1.6
3.31
2.3sin45≈1.6
F1 = < , 0.0 > +
F2 = < 1.6 , >
Fnet = < , >
3.31N at 209º

35. Homework
Problems on pages 465 and 465
#s 12, 13, 18

36. Closure
Kahoot