1. Coulomb’s law

2. Objectives Describe the historical development of the concepts of electromagnetic force. Describe and calculate how the magnitude of the electric force between two objects depends on their charges and the distance between them.

3. Assessment 1.For whom was the unit of charge, the coulomb, named and in what way(s) did this person contribute to our understanding of the electric force? 2.Two charged particles are located 1.0 m apart. Describe the direction for the electric force between them if the two charges are: a.+1 μC and +1 μC b.+1 μC and -1 μC c.-1 μC and -1 μC

4. a)Calculate the magnitude of the electric force between them if the two charges are +1.0 μC and +1.0 μC. a)What would be the magnitude of the force if the charges were 50 centimeters apart? 3.Two charged particles are located 1.0 m apart. Assessment

5. Physics terms Coulomb’s law coulomb

6. The force between point charges is proportional to the product of the charges, divided by the square of the distance between them. Equations

7. All ordinary matter is made of atoms, and all atoms contain charged particles. Where does charge come from? The atomic nucleus contains positively-charged protons. Outside of the nucleus are tiny fast-moving, negatively charged particles called electrons.

8. Where does charge come from? The charge of an electron and proton are exactly equal and opposite. A complete atom has equal numbers of protons and electrons. Therefore, a complete atom has no net electric charge.

9. The unit of electric charge The unit of electric charge is the coulomb (C) in honor of Charles- Augustin de Coulomb (1736-1806). Coulomb was a French physicist who made the first accurate measurements of electric force between charges.

10. How big is a Coulomb? One coulomb equals the charge of 6 × 10 18 electrons or protons. Ordinary static electricity results from net charges of less than a millionth of a coulomb. A coulomb is a very large amount of charge.

11. Think: How can you increase the repulsive force between two positive charges? What does this force depend on? FeFe FeFe

12. Think: FeFe FeFe It depends on the magnitude of each charge, and the distance between them. Can you guess the formula for F e ? How can you increase the repulsive force between two positive charges? What does this force depend on? q1q1 q2q2 r

13. Coulomb’s law quantifies the electric force: where: Coulomb’s law F e = electrostatic force (N) k e = Coulomb constant = 9.0×10 9 Nm 2 /C 2 q 1 = electric charge of object 1 (C) q 2 = electric charge of object 2 (C) r = distance between the two objects (m)

14. Stating Coulomb’s law in words: The force between two charges equals the product of the charges divided by the square of the distance between them, all multiplied by a constant, k e. Coulomb’s law

15. F e increases with charge The electric force increases with increasing charge:

16. F e increases with charge Doubling one charge doubles the force: The electric force increases with increasing charge:

17. F e increases with charge Doubling one charge doubles the force: Doubling both charges quadruples the force: The electric force increases with increasing charge:

18. The electric force varies inversely with the square of the distance between charges. F e obeys an inverse square law

19. The electric force varies inversely with the square of the distance between charges. F e obeys an inverse square law DOUBLING the distance reduces the force by a factor of ¼.

20. The electric force varies inversely with the square of the distance between charges. F e obeys an inverse square law HALVING the distance increases the force by a factor of 4. DOUBLING the distance reduces the force by a factor of ¼.

21. Test your knowledge Two +1.0 μC charges are separated by a distance of 1.0 cm. What is the magnitude and direction of their mutual electric force? Asked: Given: r Relationships: Solution:

22. Asked: force Given: charge q 1 and q 2, distance r Relationships: Solution: Two +1.0 μC charges are separated by a distance of 1.0 cm. What is the magnitude and direction of their mutual electric force? Test your knowledge The force is repulsive.

23. The electric force, F e The electric force is enormously strong: One drop of water contains about 2,000 C of positive and negative charges. If you could separate these charges by one meter...

24. The electric force is enormously strong: One drop of water contains about 2,000 C of positive and negative charges. If you could separate these charges by one meter, they would attract each other with a force of 36,000,000,000,000,000 N. The electric force, F e Most applications in electrostatics involve small amounts of charge, often expressed as micro-coulombs (μC = 10 -6 Coulombs).

25. The electric forces between elementary particles are much much greater than their gravitational attraction. Comparing forces: F e and F g

26. The electric forces between elementary particles are much much greater than their gravitational attraction. The force of gravity is so much smaller in these situations that we say it is negligible—meaning you can ignore it. Comparing forces: F e and F g

27. Assessment 1.For whom was the unit of charge, the coulomb, named and in what way(s) did this person contribute to our understanding of the electric force?

28. Assessment 1.For whom was the unit of charge, the coulomb, named and in what way(s) did this person contribute to our understanding of the electric force? answer: Charles-Augustin de Coulomb (1736-1806) was a French physicist who made the first accurate measurements of the electrical force between charges.

29. Assessment 2.Two charged particles are located 1.0 m apart. Describe the direction for the electric force between them if the two charges are: a.+1 μC and +1 μC b.+1 μC and -1 μC c.-1 μC and -1 μC

30. 2.Two charged particles are located 1.0 m apart. Describe the direction for the electric force between them if the two charges are: a.+1 μC and +1 μC repulsive b.+1 μC and -1 μC attractive c.-1 μC and -1 μC repulsive Assessment

31. a)Calculate the magnitude of the electric force between them if the two charges are +1.0 μC and +1.0 μC. 3.Two charged particles are located 1.0 m apart. Assessment

32. a)Calculate the magnitude of the electric force between them if the two charges are +1.0 μC and +1.0 μC. a)What would be the magnitude of the force if the charges were 50 centimeters apart? Assessment 3.Two charged particles are located 1.0 m apart.

33. a)Calculate the magnitude of the electric force between them if the two charges are +1.0 μC and +1.0 μC. a)What would be the magnitude of the force if the charges were 50 centimeters apart? Four times as strong: 0.036 N Assessment 3.Two charged particles are located 1.0 m apart.