Electrostatics

1. Electrostatics July 13, 2014

2. Atomic Charges • 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.

3. Charge • Charge comes in two forms, which Ben Franklin designated as positive (+) and negative(–). • Charge is quantized • It only comes in packets • The smallest possible stable charge, which we designate as e, is the magnitude of the charge on 1 electron or 1 proton. • e is referred to as the “elementary” charge. • e = 1.602 × 10-19 Coulombs. • We say a proton has charge of e, and an electron has a charge of –e.

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

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

6. 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?

7. Coulomb’s Law andElectrical Force

8. 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.

9. Coulomb’s Law • 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 = 9.0 × 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.

10. 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?

11. 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.

12. Electric Fields

13. 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. • We can easily calculate the electric force from the electric field.

14. Electric 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.

15. Field Lines Around Charges • 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.

16. 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!

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

18. 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?

19. 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?

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

21. Electric Fields • The Electric Field surrounding a point charge or a spherical charge can be calculated by: • E = kq / 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)

22. Superposition of Fields • 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.

23. Electric Field Lines • 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.

24. 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?

25. 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?

26. Electric Potential

27. 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. • The unit is the Joule.

28. Electric Potential Energy • Electrical potential energy increases when charges are brought into less favorable configurations + - - -

29. Electric Potential Energy • Electrical potential energy decreases when charges are brought into more favorable configurations. + + + -

30. Work • Work must be done on the charge to increase the electric potential energy.

31. Electric Potential • Electric potential is hard to understand, but easy to measure. • We commonly call it “voltage”, and its unit is the Volt. • 1 V = 1 J/C • Electric potential is easily related to both the electric potential energy, and to the electric field.

32. Electric Potential • The change in potential energy is directly related to the change in voltage. • ΔU = q Δ V • Δ U: change in electrical potential energy (J) • q: charge moved (C) • Δ V: potential difference (V) • All charges will spontaneously go to lower potential energies if they are allowed to move.

33. Electric Potential • Since all charges try to decrease U, and ΔU = q ΔV, this means that spontaneous movement of charges result in negative ΔU. • V = U / q • Positive charges like to DECREASE their potential (ΔV < 0) • Negative charges like to INCREASE their potential. (ΔV > 0)

34. Problem • A 3.0 μC charge is moved through a potential difference of 640 V. What is its potential energy change?

35. E-field & Potential • The electric potential is related in a simple way to a uniform electric field. • ΔV = -Ed • ΔV: change in electrical potential (V) • E: Constant electric field strength (N/C or V/m) • d: distance moved (m)

36. Problem • An electric field is parallel to the x-axis. What is its magnitude and direction of the electric field if the potential difference between x =1.0 m and x = 2.5 m is found to be +900 V?

37. More Electric Field Stuff

38. Excess Charges • Excess charges reside on the surface of a charged conductor. • If excess charges were found inside a conductor, they would repel one another until the charges were as far from each other as possible, thus the surface.

39. Charge Location • Electric field lines are more dense near a sharp point, indicating the electric field is more intense in such regions. • All lightning rods take advantage of this by having a sharply pointed tip. • During an electrical storm, the electric field at the tip becomes so intense that charge is given off into the atmosphere, discharging the area near a house at a steady rate and preventing a sudden blast of lightning.

40. E-Field of a Charged Sphere • The electric field inside a conductor must be zero. + E=0 + + + + + + + + + + + +

41. - E=0 + - + - + + - + - + - + Conductor in an E-Field • The electric field inside a conductor must be zero.

42. Electric Potential Energy

43. Conservation of Energy • In a conservative system, energy changes from one form of mechanical energy to another. • When only the conservative electrostatic force is involved, a charged particle released from rest in an electric field will move so as to lose potential energy and gain an equivalent amount of kinetic energy. • The change in electrical potential energy can be calculated by • ΔU = qΔV.

44. Problem • If a proton is accelerated through a potential difference of -2,000 V, what is its change in potential energy? • How fast will this proton be moving if it started at rest?

45. Problem • A proton at rest is released in a uniform electric field. How fast is it moving after it travels through a potential difference of -1200 V? How far has it moved?

46. Electric Potential Energy • Electric potential energy is a scalar, like all forms of energy. • U = kq1q2/r • U: electrical potential energy (J) • k: 9 × 109 N m2 / C2 • q1, q2 : charges (C) • r: distance between centers (m) • This formula only works for spherical charges or point charges.

47. Problem • How far must the point charges q1 = +7.22 μC and q2 = -26.1 μC be separated for the electric potential energy of the system to be -126 J?

48. Electric Potential • For a spherical or point charge, the electric potential can be calculated by the following formula • V = kq/r • V: potential (V) • k: 9 × 109 N m2 / C2 • q: charge (C) • r: distance from the charge (m)

49. Problem • The electric potential 1.5 m from a point charge q is 2.8 x 104 V. What is the value of q?

50. E-Field and Potential