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Electric Field

Electric Field. Point charge:. Uniformly charged sphere:. y. for r>R (outside). for r<R (inside). x. Dipole:. for r>>s :. at <r,0,0>. z. s. at <0,r,0>. -q. +q. at <0,0,r>. Dipole moment: p = qs. Clicker Question 1. s. - e. + 2e.

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Electric Field

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  1. Electric Field Point charge: Uniformly charged sphere: y for r>R (outside) for r<R (inside) x Dipole: for r>>s : at <r,0,0> z s at <0,r,0> -q +q at <0,0,r> Dipole moment: p = qs

  2. Clicker Question 1 s -e +2e What is the magnitude of the net electric field at location X, due to these two charges? Assume d >> s d X What is the approximate magnitude?

  3. Clicker Question 2 Locations A, B, and Care equidistant from the center of the dipole (charges +qand–qare separated by s). At which location(s) is the magnitude of the electric field approximately ? at location A at location B at location C at locations A, C at locations A, B, C d - + A d d B C

  4. Clicker Question 3 What is the direction of the electric field at location X, due to the dipole? - + C B D X E A

  5. Clicker Question

  6. Clicker Question

  7. Clicker Question

  8. Choice of System Multiparticle systems: Split into objects to include into system and objects to be considered as external. • To use field concept instead of Coulomb’s law we split the Universe into two parts: • the charges that are the sources of the field • the charge that is affected by that field

  9. A Fundamental Rationale • Convenience: know E at some location – know the electric force on any charge: • Electric properties of matter– independent of how this field was produced. Example: if E > 3106 N/C air becomes a conductor • Retardation • Nothing can move faster than light c • c = 300,000 km/s = 30 cm/ns Coulomb’s law is not completely correct – it does not contain time t nor speed of light c. v<<c !!!

  10. Chapter 15Matter and Electric Fields

  11. Net Charge 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

  12. Conservation of Charge 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. The net electric charge is conserved in any physical process. Charge can be transferred from one object to another. Pair-Production:

  13. The Structure of an Atom Hydrogen 10-10 m (1 Å) Nucleus, ~10-15 m Charge of electron cloud equals that of nucleus  neutral atom. If the electron cloud is centered on the nucleus  electric field produced by electrons exactly cancels the field produced by nucleus.

  14. Polarization of Atoms E + - + Force due to E created by positive charge shifts electron cloud and nucleus in opposite directions: electric dipole. An atom is said to be polarized when its electron cloud has been shifted by the influence of an external charge so that the electron cloud is not centered on the nucleus.

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

  16. Polarization Amount of polarization p in most materials is proportionalto 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. E E

  17. A Neutral Atom and a Point Charge 1. Charge q1 creates field E1 at the location of the atom

  18. A Neutral Atom and a Point Charge 1) 2. Field E1 polarizes the atom creating a dipole

  19. A Neutral Atom and a Point Charge 1) 2) 3. Dipole creates field E2 at the location of q1

  20. A Neutral Atom and a Point Charge 1) 3) 2) 4. Induced dipole exerts force F1 on the charge:

  21. A Neutral Atom and a Point Charge 1) 3) 2) 4) 5. The charge q1exerts force F2 on the dipole (reciprocity):

  22. A Neutral Atom and a Point Charge 1) 2) 3) 4) 5) Neutral atoms are attracted by charges! Interaction strength ~ 1/r5

  23. Exercise FA - + FB - + 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

  24. Interaction of Charged Tapes and Neutral Matter

  25. Interaction of like-charged Objects q1 q2 FR FA Conductor Plastic Repulsion: Attraction: Total:

  26. Determining the Charge of an Object Suppose tape is negatively charged, and you rub a wooden pencil on a wool sweater and bring it near the tape. - -  - - - If tape swings toward the pencil, does it show that the pencil had been charged positively? NOT NECESSARILY! Attraction: can happen for like-charged objects! Repulsion: can happen only for like-charged objects!

  27. Electric Field Through Intervening Matter F F The field appears to be weaker in presence of intervening (polarizable) object. Both tapes are attracted to paper Superposition principle:the presence of matter does not affect the electric field produced by a charged object. Intervening matter does not“block” the E field The resulting field is a superpositionof two fields: Field of the other charge plus the field of induced dipoles.

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