Phys1101 (P10D)

1. Phys1101 (P10D) Electricity and Magnetism

2. Review

3. Review: Class Objectives • Briefly reintroduce the basic electrostatic concepts for points charges: electric force, field strength. • Give examples of the electric force and field strength for simple configurations. • Give the example of the mechanics of calculating the electric field for the special case of the electric dipole.

4. Review: Student Objectives • Understand how to set up problems for basic electrostatic concepts for points charges: electric force, field strength. • You should be able to calculate the electric force and field strength for simple configurations.

5. Review: Student Objectives • You should be able to draw free body diagrams for all problems. • You should be able to apply the problem solving concepts to any given problem (Understand that the same problem solving technique is used for all problems!).

6. Electric Charge Discrete charge distributions

7. Introduction • Previous Knowledge: • Electric Force for point charges • Electric fields for point charges

8. Introduction • Previous Knowledge: • Electric Force for point charges • Electric fields for point charges • However we want to extend these techniques for continuous distributions. Eg. Discs and lines of charge.

9. Electric Charge • Review: • There are two types of charge – positive and negative. • All objects have a charge! • If there is an equal amount of each type, the object is neutral.

10. Electric Charge • Charge with the same sign repel. Opposite sign charge attract. • Charge is quantised. That is, it comes in discrete quantities. • The fundamental charge e = • All other quantities are multiples of

11. Electric Charge • Charge is conserved.

12. Electric Charge

13. Electric Charge Coulomb’s Law

14. Coulomb’s Law • The interaction between charged particles is described by Coulomb’s Law. • For two charged particles with charge q1 and q2 with separation r, the electrostatic force of attraction or repulsion is directly proportional to the product of their charges and inversely proportional to the square of their separation.

15. Coulomb’s Law

16. Coulomb’s Law • NB: Coulomb’s Law is of similar form to the gravitational Law, • An indication of it’s validity.

17. Coulomb’s Law • The electrostatic force obeys the law of superposition. • So that, the force on a charge due to a group of charges is the vector sum due to each charge separately.

18. q1 q2 + - q3 q4 + + Coulomb’s Law • The electrostatic force obeys the law of superposition. • So that, the force on a charge due to a group of charges is the vector sum due to each charge separately.

19. Coulomb’s Law • So that in general,

20. Coulomb’s Law • So that in general, • Recommended website: • http://hyperphysics.phy-astr.gsu.edu/ hbase/electric/elecforce.html

21. Coulomb’s Law Solving problems with Coulomb’s Law

22. Coulomb’s Law • Problem Solving Technique. • Draw a free body diagram. • Indicate only the forces acting on the particular particle and their direction.

23. q1 q2 + + r Coulomb’s Law • Example: • The figure shows two positive charges fixed in place along the x-axis. q1 and q2 . Their separation is . What is the magnitude and direction of the electrostatic force on particle1 from particle2?

24. q1 q2 + + r Coulomb’s Law • Since particles have the same charge they will repel. + F12 q1

25. q1 q2 + + r Coulomb’s Law • Since particles have the same charge they will repel. + F12 q1

26. + F12 q1 q1 q2 + + r Coulomb’s Law • Since particles have the same charge they will repel.

27. Coulomb’s Law • In unit vector notation:

28. The Electric Field

29. The Electric Field • An electric field exists at a point if an electric force F, is exerted on a test charge q0 placed at that point. • The electric field can be defined as: • The electric force per unit charge.

30. E F + The Electric Field • The direction of is the direction of the force acting on the positive test charge.

31. E F + The Electric Field • The direction of is the direction of the force acting on the positive test charge. • NB: the field is produced independent of the test charge.

32. The Electric Field • The electric field due to a point charge is given by

33. The Electric Field • The principle of superposition also holds for electric fields. Therefore

34. The Electric Field • Example: Three particles with charge q1=+2Q, q2 =-2Q and q3 =-4Q each a distances d from the origin. What is the net electric field at the origin? q1 q3 + - d d d q2 -

35. The Electric Field • Solution: E3 q1 q3 + - d d E2 d E1 q2 -

36. The Electric Field • Solution: E3 E3 E2 E1 E1+ E2

37. The Electric Field • Solution: E3 E3 E2 E1 E1+ E2

38. E3x E1x+ E2x The Electric Field • We decompose the vectors into components. • In this case the components in the y-direction cancel. • The only components are in x-direction (both in the positive x-direction).

39. E3x E1x+ E2x The Electric Field • Solution:

40. +q + d -q - Electric Dipole • The configuration of two oppositely charged particles with magnitude q and separation d is called a dipole.

41. Electric Dipole: Interlude • The same technique used for the example on slide 34 is used to calculate the electric field of the dipole. • The net electric field is the vector sum of the electric field due to each charge.

42. P r(+) r(-) +q + d -q - Electric Dipole • The configuration of two oppositely charged particles with magnitude q and separation d is called a dipole. • Let’s calculate the electric field at a point p.

43. P r(+) r(-) z +q + d -q - Electric Dipole • The particles are chosen along the z axis.

44. P E(+) r(+) E(-) r(-) z +q + d -q - Electric Dipole • The particles are chosen along the z axis. Because of symmetry the electric field for each charge is along the z axis.

45. E(+) P E(-) r(+) z r(-) +q + d -q - Electric Dipole • The resultant electric field E is:

46. E(+) P E(-) r(+) z r(-) +q + d -q - Electric Dipole • The resultant electric field E is:

47. E(+) P E(-) r(+) z r(-) +q + d -q - Electric Dipole • Note:

48. E(+) P E(-) r(+) z r(-) +q + d -q - Electric Dipole • The resultant electric field E is:

49. E(+) P E(-) r(+) z r(-) +q + d -q - Electric Dipole • Taking out the common term (z) we get:

50. E(+) P E(-) r(+) Considering distances z r(-) +q We can use a binomial expansion. + d -q - Electric Dipole • Taking out the common term (z) we get: