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iClicker Quiz

iClicker Quiz. (1) I have completed at least 50% of the reading and study-guide assignments associated with the lecture, as indicated on the course schedule. a) True b) False. F app. b. a. d s. Pulling a cart through deep sand (motion parallel to force).

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iClicker Quiz

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  1. iClicker Quiz (1) I have completed at least 50% of the reading and study-guide assignments associated with the lecture, as indicated on the course schedule. a) True b) False

  2. Fapp b a ds Pulling a cart through deep sand (motion parallel to force). Force is a vector. Differential path length is a vector. Work is a scalar quantity. Only the force component along the motion direction does work.

  3. + 0 0  Work done by Fg: Work done by gravity ds

  4. m Change in gravitational potential energy = ()work done by gravity x

  5. x m Work done by gravity

  6. One mass possesses a potential. Two masses interact to have potential energy. Gravitational potential Gravitational potential is not the same as potential energy. It’s the energy/mass that a test mass would possess if present. No test mass is needed for a gravitational potential to exist.

  7. Force Potential Energy Field Potential

  8. One charge possesses a potential. Two charges interact to have potential energy. Electric potential Electric potential is not the same as potential energy. It’s the energy/charge that a test charge would possess if present. No test charge is needed for an electric potential to exist.

  9. Force Potential Energy Field Potential

  10. Force Potential Energy Field Potential

  11. Gradient: a three-dimensional derivative (three derivatives instead of one) A gradient always points in the direction of steepest ascent. An E-field always points in the direction of steepest descent.

  12. 0 V 100 V U +U - F +V V + E F +U U Vector fields point downhill in potential (V). Forces point downhill in energy (U).

  13. 0 V 1 V E b e a An electron (or protron) passing through a 1 Volt potential difference experiences a 1 electron-Volt (eV) change in potential energy. Static E-fields are conservative, which implies that the potential difference between two points is independent of the path travelled!

  14. E 0 V 1 V e A free charge passing through a potential difference will experience a change in kinetic energy opposite to its change in potential energy.

  15. Consider moving a positive test between the following points on the equipotential surfaces shown. (1) A-B (2) B-C (3) C-D (4) D-E Which way does the field point? Quiz: Which movement involves no work? Quiz: Which movement requires us to do the most positive work? Quiz: Which movement lowers the potential energy the most?

  16. Special case: point charge Force Potential Energy Field Potential

  17. + negative test charge  Electric potential near point charges Which way will the field point? (a) +x (b) x (c) +y (d) y Which way will the force point? (a) +x (b) x (c) +y (d) y

  18. r R: ∞ → r Point-charge example: use E to obtain V.

  19. Example of a potential gradient calculation

  20. Point-charge example: use V to obtain E.

  21. Potential from a conducting sphere with charge Q on the surface

  22. E V Potential: positively-charged conducting shell, or an insulating shell with uniform surface charge density

  23. y (1,1,1) x (1,0,1) z V(1,1,1) = 10 Volts Find V(1,0,1)

  24. V(0,0,0) = 0 Volts Find V(1,1,1) z y x

  25. 0 0 Infinite line charge E Neither zero nor infinity are convenient zero-voltage references.

  26. Field lines and equipotential surfaces for a few simple configurations: uniform, monopole, and dipole fields. Equipotential surfaces are pendicular to the field lines at every point, and densely spaced when the field lines are densely spaced. They are like elevation contours on a topographical map – it marks a region of constant voltage (height).

  27. Quiz: Where is the electric potential greatest? http://geology.isu.edu/geostac/Field_Exercise/topomaps/

  28. p

  29. In electrostatic equilibrium, conducting objects are equi-potential bodies, and therefore have equipotential surfaces.

  30. Despite a complicated surface charge density, the entire surface of the conducting sphere has the same potential.

  31. a Insulating ring of radius a and linear charge density 

  32. Insulating annulus with uniform surface charge density , inner radius a and outer radius b

  33. Potential from a conducting sphere with charge Q on the surface dQ

  34. E V Point charge potential

  35. E V Potential: positively-charged solid conducting sphere

  36. E V Potential: positively-charged conducting shell, or an insulating shell with uniform surface charge density

  37. E V Potential: positively-charged solid insulating sphere

  38. E V Positive point charge within a thick neutral conducting shell

  39. V E Negative point charge within a thick neutral conducting shell

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