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Physics 2220

Physics 2220. Physics for Scientists and Engineers II. Chapter 23: Electric Fields. Materials can be electrically charged. Two types of charges exist: “ Positive ” and “ Negative ”. Objects that are “charged” either have a net “positive” or a net “negative” charge residing on them.

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Physics 2220

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  1. Physics 2220 Physics for Scientists and Engineers II Physics for Scientists and Engineers II , Summer Semester 2009

  2. Chapter 23: Electric Fields • Materials can be electrically charged. • Two types of charges exist: “Positive” and “Negative”. • Objects that are “charged” either have a net “positive” or a net “negative” charge residing on them. • Two objects with like charges (both positively or both negatively charged) repel each other. • Two objects with unlike charges (one positively and the other negatively charged) attract each other. • Electrical charge is quantized (occurs in integer multiples of a fundamental charge “e”). q =  N e (where N is an integer) electrons have a charge q = - e protons have a charge q = + e neutrons have no charge Physics for Scientists and Engineers II , Summer Semester 2009

  3. Material Classification According to Electrical Conductivity • Electrical conductors: Some electrons (the “free” electrons) can move easily through the material. • Electrical insulators: All electrons are bound to atoms and cannot move freely through the material. • Semiconductors: Electrical conductivity can be changed over several orders of magnitude by “doping” the material with small quantities of certain atoms, making them more or less like conductors/insulators. Physics for Scientists and Engineers II , Summer Semester 2009

  4. + + + + + + + + + + - - - - - - - - - - - - - - - - Shifting Charges in a Conductor by “Induction” uncharged metal sphere Negatively charged rod Left side of metal sphere more positively charged Right side of metal sphere more negatively charged Physics for Scientists and Engineers II , Summer Semester 2009

  5. Coulomb’s Law (Charles Coulomb 1736-1806) Magnitude of force between two “point charges” q1 and q2 . Coulomb constant r = distance between point charges Permittivity of free space Physics for Scientists and Engineers II , Summer Semester 2009

  6. Charge Unit of charge = Coulomb Smallest unit of free charge: e = 1.602 18 x 10-19 C Charge of an electron: qelectron = - e = - 1.602 18 x 10-19 C Physics for Scientists and Engineers II , Summer Semester 2009

  7. Vector Form of Coulomb’s Law Force is a vector quantity(has magnitude and direction). unit vector pointing from charge q1to charge q2 Force exerted by charge q1on charge q2 (force experienced by charge q2 ). Physics for Scientists and Engineers II , Summer Semester 2009

  8. Vector Form of Coulomb’s Law Force is a vector quantity(has magnitude and direction). unit vector pointing from charge q2to charge q1 Force exerted by charge q2on charge q1 (force experienced by charge q1 ). Physics for Scientists and Engineers II , Summer Semester 2009

  9. + + + Directions of forces and unit vectors q2 - q2 q1 q1 Physics for Scientists and Engineers II , Summer Semester 2009

  10. + + Calculating the Resultant Forces on Charge q1 in a Configuration of 3 charges a = 1cm q1 q2 0.5 cm 0.5 cm q3 - q3 = - 2.0 mC q1 = q2 =+2.0 mC Physics for Scientists and Engineers II , Summer Semester 2009

  11. q1 q2 - + + Forces acting on q1 q3 Total force on q1: Physics for Scientists and Engineers II , Summer Semester 2009

  12. Magnitude of the Various Forces on q1 Note: I am temporarily carrying along extra significant digits in these intermediate results to avoid rounding errors in the final result. Physics for Scientists and Engineers II , Summer Semester 2009

  13. q1 q2 - + + Adding the Vectors Using a Coordinate System y q3 x Physics for Scientists and Engineers II , Summer Semester 2009

  14. Adding the Vectors Using a Coordinate System y x Physics for Scientists and Engineers II , Summer Semester 2009

  15. …doing the algebra… F1 has a magnitude of Physics for Scientists and Engineers II , Summer Semester 2009

  16. Calculating the force on q2 … another example using an even more mathematical approach Charges Location of charges q1 = +3.0 mC x1=3.0cm ; y1=2.0cm ; z1=5.0cm q2 = - 4.0 mC x2=2.0cm ; y2=6.0cm ; z2=2.0cm In this example, the location of the charges and the distance between the charges are harder to visualize  Use a more mathematical approach! Physics for Scientists and Engineers II , Summer Semester 2009

  17. Calculating the force on q2 … another example using an even more mathematical approach d12=distance between q1 and q2. Physics for Scientists and Engineers II , Summer Semester 2009

  18. - + Calculating the force on q2 … mathematical approach We need the distance between the charges. d12 is distance between q1 and q2. y q1 q2 x z Physics for Scientists and Engineers II , Summer Semester 2009

  19. Calculating the force on q2 … mathematical approach Distance between charges q1 and q2 . Physics for Scientists and Engineers II , Summer Semester 2009

  20. - + Calculating the force on q2 … mathematical approach We need the unit vectors between charges. For example, the unit vector pointing from q1to q2 is easily obtained by normalizing the vector pointing from from q1 to q2. y q1 q2 x z Physics for Scientists and Engineers II , Summer Semester 2009

  21. Calculating the force on q2 … mathematical approach The needed unit vector: Physics for Scientists and Engineers II , Summer Semester 2009

  22. Calculating the force on q2 … mathematical approach You can easily verify that the length of the unit vector is “1”. Physics for Scientists and Engineers II , Summer Semester 2009

  23. Calculating the force on q2 … another example using an even more mathematical approach Physics for Scientists and Engineers II , Summer Semester 2009

  24. Calculating the force on q2 … another example using an even more mathematical approach …and if you want to know just the magnitude of the force on q2: Physics for Scientists and Engineers II , Summer Semester 2009

  25. 23.4 The Electric Field It is convenient to use positive test charges. Then, the direction of the electric force on the test charge is the same as that of the field vector. Confusion is avoided. Physics for Scientists and Engineers II , Summer Semester 2009

  26. 23.4 The Electric Field Q qo + + + + + test charge + + + + Source charge Physics for Scientists and Engineers II , Summer Semester 2009

  27. 23.4 The Electric Field Physics for Scientists and Engineers II , Summer Semester 2009

  28. 23.4 The Electric Field of a “Point Charge” q q0 r q Physics for Scientists and Engineers II , Summer Semester 2009

  29. 23.4 The Electric Field of a Positive “Point Charge” q (Assuming positive test charge q0) q0 + Force on test charge P + Electric field where test charge used to be (at point P). The electric field of a positive point charge points away from it. Physics for Scientists and Engineers II , Summer Semester 2009

  30. 23.4 The Electric Field of a Negative “Point Charge” q (Assuming positive test charge q0) q0 - Force on test charge P - Electric field where test charge used to be (at point P). The electric field of a negative point charge points towards it. Physics for Scientists and Engineers II , Summer Semester 2009

  31. 23.4 The Electric Field of a Collection of Point Charges Physics for Scientists and Engineers II , Summer Semester 2009

  32. 23.4 The Electric Field of Two Point Charges at Point P y P y q1 q2 x a b Physics for Scientists and Engineers II , Summer Semester 2009

  33. 23.4 The Electric Field of Two Point Charges at Point P y P Pythagoras: r1 r2 y a b x q1 q2 Physics for Scientists and Engineers II , Summer Semester 2009

  34. 23.4 The Electric Field of Two Point Charges at Point P y P x q1 q2 Physics for Scientists and Engineers II , Summer Semester 2009

  35. 23.4 The Electric Field of Two Point Charges at Point P Physics for Scientists and Engineers II , Summer Semester 2009

  36. 23.4 The Electric Field of Two Point Charges at Point P Special case: q1= q and q2 = -q AND b = a E from + charge E from - charge - + q -q Physics for Scientists and Engineers II , Summer Semester 2009

  37. 23.4 The Electric Field of Two Point Charges at Point P Special case: q1= q and q2 = q AND b = a E from other + charge E from + charge + + q q Physics for Scientists and Engineers II , Summer Semester 2009

  38. This is called an electric DIPOLE Special case: q1= q and q2 = -q AND b = a E from + charge E from - charge - + q -q For large distances y (far away from the dipole), y >> a: E falls off proportional to 1/y3 Fall of faster than field of single charge (only prop. to 1/r2). From a distance the two opposite charges look like they are almost at the same place and neutralize each other. Physics for Scientists and Engineers II , Summer Semester 2009

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