Electrostatics

1. Electrostatics Charge and Polarization

2. ELECTROSTATICS

3. Demonstration #1 • Demonstrate how you can pick up the tissue without touching it in any way with your body. • What is occurring on the atomic level that lets you do this?

4. The atom • The atom has positive charge in the nucleus, located in the protons. The positive charge cannot move from the atom unless there is a nuclear reaction. • The atom has negative charge in the electron cloud on the outside of the atom. Electrons can move from atom to atom without all that much difficulty.

5. Question • You charge the balloon by rubbing it on hair or on a sweater, and the balloon becomes negative. How can it pick up a neutral tissue?

6. This is an electroscope The electroscope is made from a metal or other conductor, and may be contained within a flask. The vanes are free to move. Pole Vanes

7. Demonstration #2 • Rub the black rod with the fur. Bring the rod toward the pole of the electroscope. What happens to the vanes? • Come up with an atomic-level explanation for your observations.

8. Demonstration #3 • Rub the glass rod with the silk. Bring the rod toward the pole of the electroscope. What happens to the vanes? • Come up with an atomic-level explanation for your observations.

9. Demonstration #4 • What happens when you touch the electroscope with the glass rod?

10. Charge • Charge comes in two forms, which Ben Franklin designated as positive (+) and negative(–). • (Unfortunately, because electrons were yet to be discovered, Ben set the flow of electricity as the flow of POSITIVE charge, which we still use today even though we now know that is really is the flow of the negative charges from electrons! See next slide…)

11. From xkcd

12. Charge continued… • Charge is quantized (meaning increases in levels). • The smallest possible stable charge, which we designate as e, is the magnitude of the charge on 1 electron or 1 proton. • We say a proton has charge of e, and an electron has a charge of –e. • e is referred to as the “elementary” charge. • e = 1.602  10-19 Coulombs. • The coulomb is the SI unit of charge.

13. Sample Problem A certain static discharge delivers -0.5 Coulombs of electrical charge. How many electrons are in this discharge?

14. Sample Problem • How much positive charge resides in two moles of hydrogen gas (H2)? • How much negative charge? • How much net charge?

15. Sample Problem The total charge of a system composed of 1800 particles, all of which are protons or electrons, is 31x10-18 C. • How many protons are in the system? • How many electrons are in the system?

16. Coulomb’s Law and Electrical Force

17. Electric Force • Charges exert forces on each other. • Like charges (two positives, or two negatives) repel each other, resulting in a repulsive force. • Opposite charges (a positive and a negative) attract each other, resulting in an attractive force.

18. Coulomb’s Law – form 1 • Coulomb’s law tells us how the magnitude of the force between two particles varies with their charge and with the distance between them. • k = 8.99  109 N m2 / C2 • q1, q2 are charges (C) • r is distance between the charges (m) • F is force (N) • Coulomb’s law applies directly only to spherically symmetric charges.

19. Coulomb’s Law – form 2 • Sometimes you see Coulomb’s Law written in a slightly different form • eo = 8.85  10-12 C2/ N m2 • q1, q2 are charges (C) • r is distance between the charges (m) • F is force (N) • This version is theoretically derived and less practical that form 1

20. Spherically Symmetric Forces • Newton’s Law of Gravity • Coulomb’s Law

21. Sample Problem A point charge of positive 12.0 μC experiences an attractive force of 51 mN when it is placed 15 cm from another point charge. What is the other charge?

22. Sample Problem Calculate the mass of ball B, which is suspended in midair. qA = 1.50 nC A 1.3 m B qB = -0.50 nC

23. Superposition • Electrical force, like all forces, is a vector quantity. • If a charge is subjected to forces from more than one other charge, vector addition must be performed. • Vector addition to find the resultant vector is sometimes called superposition.

24. Sample Problem y (m) 2.0 • What is the force on the 4 mC charge? 1.0 -3 mC 2 mC 4 mC 1.0 2.0 x (m)

25. Sample Problem y (m) 2.0 • What is the force on the 4 mC charge? -3 mC 1.0 2 mC 4 mC 1.0 2.0 x (m)

26. The Electric Field

27. The Electric Field • The presence of + or – charge modifies empty space. This enables the electrical force to act on charged particles without actually touching them. • We say that an “electric field” is created in the space around a charged particle or a configuration of charges. • If a charged particle is placed in an electric field created by other charges, it will experience a force as a result of the field. • Sometimes we know about the electric field without knowing much about the charge configuration that created it. • We can easily calculate the electric force from the electric field.

28. Why use fields? • Forces exist only when two or more particles are present. • Fields exist even if no force is present. • The field of one particle only can be calculated.

29. Field around + charge • The arrows in a field are not vectors, they are “lines of force”. • The lines of force indicate the direction of the force on a positive charge placed in the field. • Negative charges experience a force in the opposite direction.

30. Field around ( - ) charge

31. Field between charged plates + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

32. Field Vectors from Field Lines • The electric field at a given point is not the field line itself, but can be determined from the field line. • The electric field vectors is always tangent to the line of force at that point. • Vectors of any kind are never curvy!

33. Field Vectors from Field Lines

34. Force from Electric Field • The force on a charged particle placed in an electric field is easily calculated. • F = E q • F: Force (N) • E: Electric Field (N/C) • q: Charge (C)

35. Sample Problem The electric field in a given region is 4000 N/C pointed toward the north. What is the force exerted on a 400 μg styrofoam bead bearing 600 excess electrons when placed in the field?

36. Sample Problem A 400 μg styrofoam bead has 600 excess electrons on its surface. What is the magnitude and direction of the electric field that will suspend the bead in midair?

37. Sample Problem A proton traveling at 440 m/s in the +x direction enters an an electric field of magnitude 5400 N/C directed in the +y direction. Find the acceleration.

38. For Spherical Electric Fields • The Electric Field surrounding a point charge or a spherical charge can be calculated by: • E = k q / r2 • E: Electric Field (N/C) • k: 8.99 x 109 N m2/C2 • q: Charge (C) • r: distance from center of charge q (m) • Remember that k = 1/4peo

39. Superposition

40. Principle of Superposition • When more than one charge contributes to the electric field, the resultant electric field is the vector sum of the electric fields produced by the various charges. • Again, as with force vectors, this is referred to as superposition.

41. Remember… • Electric field lines are NOT VECTORS, but may be used to derive the direction of electric field vectors at given points. • The resulting vector gives the direction of the electric force on a positive charge placed in the field.

42. Sample Problem A particle bearing -5.0 μC is placed at -2.0 cm, and a particle bearing 5.0 μC is placed at 2.0 cm. What is the field at the origin?

43. Sample Problem A particle bearing 10.0 mC is placed at the origin, and a particle bearing 5.0 mC is placed at 1.0 m. Where is the field zero?

44. Sample Problem What is the charge on the bead? It’s mass is 32 mg. E = 5000 N/C 40o

45. Electric Field Plotter Laboratory

46. The electric field and voltage • The electric field points in the direction of largest negative voltage change. • If the black lead of a voltmeter is placed at a fixed point, and the red lead is moved around at constant distance from the black lead until the largest negative reading is obtained on the voltmeter, this can be used to map the electric field at that point in space. • Using the voltmeter, you can map field lines from a + electrode to a – electrode. E -0.23

47. Electric Field Plotter Lab • Wire one painted silver electrode to the + DC outlet and the other painted silver electrode to the – DC outlet of your power supply. Your teacher will show you how to do this. Set the power supply to around 10 Volts DC. • Touch the black lead to one electrode and the red lead to the other electrode to make sure you are getting a good, steady voltage reading of around 8 to 10 Volts • Mark + by the positive electrode and – by the negative electrode. • Starting at the +electrode, map a field line by placing the black lead down on the paper and carefully rotating the red lead (at constant distance from the black lead) until the display reads a maximum negative voltage. Carefully mark the field vector at that location with a pencil. • Place the black lead at the arrowhead you just drew, and map a new field vector. • Continue marking field vectors until you arrive at the negative electrode. • You must mark several good field lines during the class period.

48. Shielding, excess charges on conductors, charging by induction, finish Electric Field lab.

49. Electric Potential and Potential Energy

50. Electric Potential Energy • Electrical potential energy is the energy contained in a configuration of charges. Like all potential energies, when it goes up the configuration is less stable; when it goes down, the configuration is more stable. • Electrical potential energy increases when charges are brought into less favorable configurations (ex:, like-sign charges getting closer together, or unlike-sign charges farther apart). • Electrical potential energy decreases when charges are brought into more favorable configurations. • The unit is the Joule.