1. Electrostatics laboratory of the 1700s

2. + + + + + + + + + + + + + + + + + + +  When the electric field is uniform, V = Ed When the electric field is NOT uniform V  Ed But for an isolated concentration of charge we have

3. +  +  ?

4. A large conducting sphere of radius R initially carries an initial charge. When touched to a smaller, uncharged conducting sphere of radius r < R charge flows to the smaller sphere until 1. each sphere carries half the total charge. 2. each sphere carries the same density of charge. 3. charge is divided between them in proportion to their radii: q/Q = r/R.

5. Two conducting spheres (radius R and r), after touching, are at the same potential. = or

6. But check out a comparison of the charge DENSITY across the surface of each: If then And how do these compare: 1. > 2. = 3. <

7. But check out a comparison of the charge DENSITY across the surface of each: Although Q > q The charge density across the surface of the smaller sphere is HIGHER! Charge is crowded together much more tightly on the smaller sphere!

8. This charged ellipsoidal conductor 1. has its electric charge uniformly distributed across its surface. 2. has denser charge packed across the broad, blunt surface at left. 3. has denser charge packed across the small, pointier end at right.

9. Consider electrons spread out across the surface:

10. A bump or imperfection on an otherwise smooth surface: A sharp point: are effectively regions with small radii and enormous electric fields!

15. If you’ve had any chemistry, you may recall electron pairs fill sub-orbitals: Hydrogen has 1 proton, 1 electron Oxygen has 8 protons, 8 electrons Two most inner orbitals are “filled.” Two outer orbitals are only “half-filled.” Oxygen is more "electronegative" or electron "loving" atom than hydrogen. (the electron affinities we discussed)

16. Two hydrogen bind with a single oxygen atom to make H 2 O. “Electronegative" oxygen shares an electron (half-time) with each hydrogen. The positive charge of the hydrogen’s nucleus is only “half-cancelled”. On average, the oxygen part of the molecule is left slightly negative.

17.       The result is a slight attraction between nearby water molecules

18. NaCl crystal                    The “polar” water molecules are attracted to…cling to the separated ions, shielding them from one another! explaining water’s role as a powerful solvent!

19. Soap and detergents are long chain molecules (animal/vegetable oils/fats or petrochemical hydrocarbon chains) with one end that ionizes in water.   The ionized end (the one that gets charged) attracts water molecules (which are always slightly polarized) “hydrophilic” The neutral end (ignored by the water molecules that crowd the hydrophilic end) is effectively water-proof. “hydrophobic”

22. Principles of static electricity explain how a Xerox copier works:

23.  An array of high voltage wire tips spray their corona discharge across a photo-conductive, semi-conducting sheet of plastic a material which conducts electricity when exposed to light, but behaves as an insulator when in the dark. charging up the sheet uniformly in the dark.

24. + + + + + + + + + + + + + + + + + + + + +  The photo-conducting sheet has a metallic backing which is grounded. + + + + + + + + + + + + + + + + +  Brightly focused spots of light selectively erases isolated spots of charge. Electrons are driven off the backing to the ground.

25. - - - - - projecting image The toner cartridge carries a mix of dry black tiny plastic flakes (the toner) and very tiny teflon-coated ball bearings generates an invisible charge image on the plastic

26. carrier ball base Applying toner

27. + + + + + + + + + + + + + + + + + + + + +  paper   Heater

29. QUESTION 1 Charge will flow between the spheres only until the voltage between them comes into balance: kQ/R = kq/r. 1. QUESTION 2 QUESTION 3 3. charge is divided: q/Q = r/R. 3. has denser charge packed across the small, pointier end at right. The only difference between these is a factor of 1/r on the left compared to 1/R on the right (the left hand side is Q/4  R  r, the right Q/4  R  R. Dividing by a big number always gives a smaller result! Charge density is only distributed uniformly across the surface of smooth, featureless spheres. Otherwise it concentrates at tight curves, sharp corners and points.