1. Chapter 15 Matter and Electric Fields

2. What is the direction of the electric field at location X, due to the dipole? Question 1 (Chap. 14) A C B E D - + X

3. Question 2 (Chap. 14) Locations 1 and 2 are equidistant from the center of the dipole. At which location is the magnitude of the electric field larger? A. at location 1 B. at location 2 C. magnitudes are the same + 1 2 d d -

5. Matter is made out of atoms. Atom contains charged particles: electrons (-e), protons (+e) Neutral atom: number of electrons and protons is equal: Example: Hydrogen atom: 1 proton, 1 electron net charge = (+e) + (-e)=0 Sodium atom: 11 protons, 11 electrons Sodium atom (Na) can lose an electron: Sodium ion (Na + ): (+11e) + (-10e) = +e Ordinary matter is electrically neutral. However, can be charged by adding/removing charged particles Net Charge Can we create an excess charge inside a sample?

6. The net charge of a system and its surroundings cannot change If one object gets charged positively, there must be an object which gets charged negatively. Conservation of Charge The net electric charge is conserved in any physical process. Charge can be transferred from one object to another.

7. it is not a permanent dipole E an induced dipole is created when a neutral object is polarized by an applied electric field An applied electric field creates induced dipoles! Induced Dipole

8. Polarization Amount of polarization p in most materials is proportional to the magnitude of the applied electric field:  - “polarizability” of a material In an induced dipole, is the distance between the charges fixed? The distance is proportional to the strength of the applied field.

9. 1. Charge q 1 creates field E 1 at the location of the atom A Neutral Atom and a Point Charge

10. 2. Field E 1 polarizes the atom creating a dipole 1) A Neutral Atom and a Point Charge

11. 3. Dipole creates field E 2 at the location of q 1 1) 2) A Neutral Atom and a Point Charge

12. 4. Induced dipole exerts force F 1 on the charge: 1) 2) 3) A Neutral Atom and a Point Charge

13. 5. The charge q 1 exerts force F 2 on the dipole (reciprocity): 1) 2) 3) 4) A Neutral Atom and a Point Charge

14. 1) 2) 3) 4) 5) Neutral atoms are attracted by charges! Interaction strength ~ 1/r 5 A Neutral Atom and a Point Charge

15. Atom A is easier to polarize than atom B. Which atom would experience a greater attraction to a point charge a distance r away? +- +- A B FAFA FBFB Exercise

16. Interaction of Charged Tapes and Neutral Matter

17. Different materials respond differently to electric field Conductor: contains mobile charges that can move through material Insulator: contains no mobile charges Conductors and Insulators

18. Insulator: Electrons are bound to the atoms or molecules. Electrons can shift slightly (<1 Å), but remain bound to the molecule. Individual atoms or molecules can be polarized by external electric field. There are a lot of molecules – the net effect produced by the induced dipoles can be very large. Polarization of Insulators

19. Diagram showing polarization of an insulator: Dipoles: exaggerated in size; stretch: degree of polarization No mobile charges: excess charges stay where they are Polarization of Insulators

20. Field E at a location of a molecule is a superposition of the external applied field and the field created by other induced dipoles: Simplifying assumption: Low Density Approximation

21. There are charges which can move freely throughout the material E In contrast to an insulator, where electrons and nuclei can move only very small distances, the charged particles in a conductor are free to move large distances. Polarization of conductors differs from that of insulators. Conductors

22. Salt water: Na + and Cl - H + and OH - Apply external electric field Ionic Solutions are Conductors (home) When an electric filed is applied to a conductor, the mobile charged particles begin to move in the direction of the force exerted on them by the field. As the charges move, they begin to pile up in one location, creating a concentration of charge  creates electric field. The net electric field is the superposition of the applied field and field created by the relocated charges.

23. Assumption: charges will move until E net =0 (static equilibrium) It is not a shielding effect, but a consequence of superposition! Proof: by contradiction: Mobile ions will move This is not equilibrium Assume E net ≠0 Assumption E net ≠0 is wrong E net =0 Ionic Solutions are Conductors (home)

24. Positive atomic cores and mobile-electron sea Electrons are not completely free – they are bound to the metal as a whole. Metal lattice There is no net interaction between mobile electrons A Model of a Metal

25. - No net interaction between mobile electrons Forget previous velocity after collision (mobility) Later we will show that conductivity (  )  μ Some important sources of collision: - impurities - thermal motion of atoms (more motion at higher temperature T  shorter  lower  [common feature of metals]) Drude Model of Electron Motion in a Metal

26. Metal in Electric Field E net inside the conductor will be: A. Uniform positive B. Uniform negative C. Zero D. will have complex pattern

27. Simplified diagram of polarized metal Metal in Electric Field Note: It is not charged! Net charge is still zero

28. In static equilibrium: E net = 0 everywhere inside the metal! Mobile charges on surface rearrange to achieve E net = 0 Actual arrangement might be very complex! It is a consequence of 1/r 2 distance dependence E net = 0 only in static equilibrium! Electric Field inside Metal

29. Excess charges in any conductor are always found on an inner or outer surface! Excess Charge on Conductors

30. ConductorInsulator Mobile chargesyesno Polarization entire sea of mobile charges moves individual atoms/molecules polarize Static equilibrium E net = 0 insideE net nonzero inside Excess chargesonly on surface anywhere on or inside material Distribution of excess charges Spread over entire surfacelocated in patches Conductors versus Insulators