1. A penny carrying a small amount of positive charge Q p exerts an electric force F on a nickel carrying a large amount of positive charge Q n that is a distance d away (Q n > Q p ). Which one of the following is not true? A. The electric force exerted on the penny by the nickel is also equal to F. B. The number of electrons in the penny is less than the number of protons in the penny. C. F=KQ p Q n /d 2, if d is small compared to the size of the coins. D. F=KQ p Q n /d 2, if d is large compared to the size of the coins. Question 1 (Chap. 14)

2. Which one of the following is not true? The electric force exerted by an electron on an electron: A. decreases by a factor of 25 if the distance is increased by a factor of 5. B. has the same magnitude as the electric force exerted by a proton on a proton at the same distance. C. has the same direction as the electric force exerted by a proton on a proton at the same distance. D. is much weaker than the gravitational force between them. Question 2 (Chap. 14)

3. The Superposition Principle

4. The E of a Uniformly Charged Sphere Can calculate using principle of superposition: for r>R (outside) for r<R (inside)

5. Electric dipole: Two equally but oppositely charged point-like objects What is the E field of the dipole? +q-q s Example of electric dipole: HCl molecule The Superposition Principle The electric field of a dipole:

6. +q-q s x y z Choice of origin: use symmetry Calculating Electric Field Choice of the origin

7. 1. E along the x-axis

8. if r>>s, then While the electric field of a point charge is proportional to 1/r 2, the electric field created by several charges may have a different distance dependence. Approximation: Far from the Dipole r =  1,0,0 

9. 2. E along the y-axis

10. if r>>s, thenat

11. 3. E along the z-axis Due to the symmetry E along the z-axis must be the same as E along the y-axis! at or at

12. Other Locations

13. Example Problem A dipole is located at the origin, and is composed of particles with charges e and –e, separated by a distance 2  10 -10 m along the x- axis. Calculate the magnitude of the E field at m. y 2Å2Å 200Å E=? Since r>>s: Using exact solution: x

14. Interaction of a Point Charge and a Dipole Direction makes sense? - negative end of dipole is closer, so its net contribution is larger What is the force exerted on the dipole by the point charge? - Newton’s third law: equal but opposite sign

15. Dipole Moment x: y, z: Dipole moment: p = qs, direction from –q to +q r>>s Dipole moment is a vector pointing from negative to positive charge The electric field of a dipole is proportional to the

16. Dipole in a Uniform Field Forces on +q and –q have the same magnitude but opposite direction It would experience a torque about its center of mass. What is the equilibrium position? Electric dipole can be used to measure the direction of electric field.

17. Neutral Matter in the Electric Field A wooden dowel rod is balanced on a sharp needle and placed between a pair of parallel plates connected to an electrostatic generator. When the plates are charged, the dowel rod: A)Could not care less B)Will orient perpendicular to the direction of the E – field C) Will orient parallel to the direction of the E – field D)Will jump out of the area with E-field

18. + 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. +- Polarization of Atoms

19. 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

20. 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

21. Convenience: know E at some location – know the electric force on any charge. Example: if E>3  10 6 N/C air becomes conductor Retardation Nothing can move faster than light c c = 300,000 km/s = 30 cm/ns Can describe the electric properties of matter in terms of electric field – independent of how this field was produced. Coulomb’s law is not completely correct – it does not contain time t nor speed of light c. v<<c !!! A Fundamental Rationale

22. The Electric Field + - Point Charge: Dipole: for r>>s : at +q -q s x y z at