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5) Coulomb’s Law

5) Coulomb’s Law. form. “Define” coulomb (C) as the quantity of charge that produces a force of 9 x 10 9 N on objects 1 m apart. b) Units Two possibilities: - define k and derive q (esu) - define q and derive k (SI) √.

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5) Coulomb’s Law

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  1. 5) Coulomb’s Law • form

  2. “Define” coulomb (C) as the quantity of charge that produces a force of 9 x 109 N on objects 1 m apart. b) Units Two possibilities: - define k and derive q (esu) - define q and derive k (SI) √

  3. For practical reasons, the coulomb is defined using current and magnetism giving k = 8.988 x 109 Nm2/C2 • Permittivity of free space Then

  4. c) Fundamental unit of charge e = 1.602 x 10-19 C

  5. Example: Force between two 1 µC charges 1 mm apart F = kq1q2/r2 = 9•109(10-6)2/(10-3)2 N = 9000 N • ~weight of 1000-kg object (1 tonne)) • same as force between two 1-C charges 1 km apart

  6. m, e m, e Fg FC Example: Coulomb force vs gravity for electrons FC = ke2/r2 FN = Gm2/r2 Ratio:

  7. Example: Velocity of an electron in the Bohr Atom Coulomb force: F = kq1q2/r2(attractive) Circular motion requires: F = mv2/r So, v2 = kq1q2/mr For r = 5.29 x 10-11m, v = 2.18 x 106 m/s

  8. d) Superposition of electric forces Net force is the vector sum of forces from each charge F3 q1 F q2 F2 q q3 F1 Net force onq: F = F1+ F2 + F3

  9. 6) Electric Field - abstraction - separates cause and effect in Coulomb’s law a) Definition Units: N/C

  10. q0 F r Coulomb’s law: Electric Field: Q b) Field due to a point charge direction is radial

  11. E3 q1 E q2 E2 q3 E1 c) Superposition of electric fields Net field is the vector sum of fields from each charge P Net field at P: E = E1+ E2 + E3

  12. D=3m d P 16 µC 4 µC q1 q2 E1 E2 P Example Find d to give E = 0 at P

  13. 7) Electric Field Lines (lines of force) a) Direction of force on positive charge radial for point charges out for positive (begin) in for negative (end)

  14. 2Q Q b) Number of lines proportional to charge

  15. E? c) Begin and end only on charges; never cross

  16. Line density at radius r: d) Line density proportional to field strength Lines of force model <==> inverse-square law

  17. 8) Applications of lines-of-force model a) dipole

  18. b) two positive charges

  19. c) Unequal charges

  20. E + + + + + + + + + + + + q, A Field is uniform and constant to ∞, in both directions d) Infinite plane of charge Electric field is proportional to the line density, and therefore to the charge density, =q/A By comparison with the field from a point charge, we find:

  21. E+ E+ E+ - + - + E- E- E- - + E=2E+ EL=0 - + - + - + e) Parallel plate capacitor (assume separation small compared to the size) ER=0 • Strong uniform field between: • Field zero outside

  22. • Fringing fields near the edges

  23. + + + + + + + + • Symmetry ==> radial • number of lines prop. to charge f) Spherically symmetric charge distribution Outside the sphere: as though all charge concentrated at the centre (like gravity)

  24. E1 E1 E2 9) Electric Fields and Conductors • Excess charge resides on surface at equilibrium • Field inside is zero at eq’m; charges move until |E1| = |E2|

  25. E E = 0 • Closed conductor shields external fields

  26. • Field lines perpendicular at surface • Field outside conducting shell not shielded

  27. Field outside grounded shell is shielded • Field larger for smaller radius E = kq/r2 (concentrated at sharp tips)

  28. Demonstration: Van de Graaf generator • purpose: to produce high field by concentrating charge -- used to accelerate particles for physics expts • principle: charge on conductors moves to the surface

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