Charge Conservation and Polarization

Transcription

1 Charge Conservation and PHYS David Blasing Wednesday June 18th, 2014

2 Quiz!!!!!!!!! On a half sheet up paper, write a main (red) result that we have seen so far in the course. 1 point for the name of the result 1 point for the formula/description 2/25

3 Our Road Map 3/25

4 Brief Review of Last Lecture : Principal of Superposition The net electric field at a location is the vector sum of every electric field made there by all the other charged particles around. E Far From the Dipole, On or Perpendicular to its Axis E = 1 p 4πɛ 0 E y 3 axis = 1 2p 4πɛ 0 r 3 4/25

5 Charge is Conserved Charge Conservation Charging Objects Charge is Conserved The total (net sum) amount of charge in the system and its surroundings does not change. 5/25

6 Charge is Conserved Charge Conservation Charging Objects Charge is Conserved The total (net sum) amount of charge in the system and its surroundings does not change. So if one part of a system becomes positively charged, then another part of the system had to acquire an equal in magnitude amount of negative charge. 5/25

7 Charge is Conserved Charge Conservation Charging Objects Charge is Conserved The total (net sum) amount of charge in the system and its surroundings does not change. So if one part of a system becomes positively charged, then another part of the system had to acquire an equal in magnitude amount of negative charge. A neutral object has a net charge of 0. 5/25

8 Examples of Neutral Atoms Charge Conservation Charging Objects Neutral atoms: number of electrons and protons is equal Examples: 1 Hydrogen atom: 1 proton, 1 electron = net charge Q tot = (+e) + (-e)=0 2 Sodium atom: 11 protons, 11 electrons = Q tot = 0 6/25

9 Examples of Neutral Atoms Charge Conservation Charging Objects Neutral atoms: number of electrons and protons is equal Examples: 1 Hydrogen atom: 1 proton, 1 electron = net charge Q tot = (+e) + (-e)=0 2 Sodium atom: 11 protons, 11 electrons = Q tot = 0 Ordinary matter is electrically neutral but often it can be charged by adding/removing charged particles 6/25

10 Charge Conservation Charging Objects Objects can be charged in many ways Note: only positive or negative ions, or electrons can be transferred by rubbing It takes an enormous amount to remove bare nuclei or protons from atoms not on the surface 7/25

11 Clicker Question 1 Charge Conservation Charging Objects 8/25

12 Clicker Question 2 Charge Conservation Charging Objects 9/25

13 Clicker Question 3 Charge Conservation Charging Objects 10/25

14 Hydrogen. Charge of electron cloud equals that of the nucleus so hydrogen is electrically neutral If the electron cloud is centered on the nucleus then the hydrogen produces no E field outside 11/25

15 : Polarized Atom An atom is polarized when its electron cloud is shifted by an external electric field and is no longer centered on the nucleus Induced polarization (i.e. an induced dipole) is not permanent. Induced dipoles appear (disappear) by the presence (absence) of a local E field. 12/25

16 Hydrogen Polarizes in an E field The E field of the positive charge exerts opposite in direction forces on the electron cloud and nucleus, creating an electric dipole. 13/25

17 Vector In the material s we will consider, the polarization is proportional to the local E (this is not true of all materials). 14/25

18 Vector In the material s we will consider, the polarization is proportional to the local E (this is not true of all materials). Vector p = α E Polarizability The proportionality between the local E and the amount of polarization is denoted α and is called the material s polarizability. 14/25

19 Dimensional Analysis α has dimensions of Cm N/C and that makes p have units of Cm. You have actually seen p before, but we didn t call it polarization. Anyone remember where? 15/25

20 Dimensional Analysis α has dimensions of Cm N/C and that makes p have units of Cm. You have actually seen p before, but we didn t call it polarization. Anyone remember where? It was the combination q s in dipoles. p = α E = q s 15/25

21 Dimensional Analysis α has dimensions of Cm N/C and that makes p have units of Cm. You have actually seen p before, but we didn t call it polarization. Anyone remember where? It was the combination q s in dipoles. p = α E = q s Is the size an induced dipole constant? 15/25

22 Dimensional Analysis α has dimensions of Cm N/C and that makes p have units of Cm. You have actually seen p before, but we didn t call it polarization. Anyone remember where? It was the combination q s in dipoles. p = α E = q s Is the size an induced dipole constant? No, it depends on the strength of the applied electric field. If there is no local E, then there is no local p! 15/25

23 Example Question: If q=e, what is the charge separation by applying a field E = N C? (This size E may cause a spark). 16/25

24 Example Question: If q=e, what is the charge separation by applying a field E = N C? (This size E may cause a spark). A typical atomic polarizability, α, is Cm N/C. 16/25

25 Example Question: If q=e, what is the charge separation by applying a field E = N C? (This size E may cause a spark). A typical atomic polarizability, α, is Cm N/C. p = α E = q s = s = α q E 2x10 15 m 16/25

26 Example Question: If q=e, what is the charge separation by applying a field E = N C? (This size E may cause a spark). A typical atomic polarizability, α, is Cm N/C. p = α E = q s = s = α q E 2x10 15 m About one hundred thousand smaller than the atom itself...a very small shift for a sizeable electric field. 16/25

27 Clicker Question 4 Can a neutral object make an electric field? A. Yes B. No C. I don t like physics. 17/25

28 Neutral Objects An electric dipole is a neutral object, but it does create a nonzero E field around it. Neutral objects can make nonzero electric fields. An object that is uniformly electrically neutral will not make an E field. 18/25

29 Clicker Question 5 Does a neutral object experience a force from a point charge? A. Yes, attraction. B. Yes, repulsion C. No. 19/25

30 Group Question Why does an inflated ballon with some excess charge (maybe by rubbing it against your hair), stick to a wall? 20/25

31 Force Between a Dipole and a Point Charge 21/25

32 Force Between a Dipole and a Point Charge 21/25

33 Force Between a Dipole and a Point Charge 22/25

34 Force Between a Dipole and a Point Charge 22/25

35 Force Between a Dipole and a Point Charge 23/25

36 Force Between a Dipole and a Point Charge 23/25

37 Force Between a Dipole and a Point Charge 24/25

38 Force Between a Dipole and a Point Charge 24/25

39 Force Between a Dipole and a Point Charge 25/25

40 Force Between a Dipole and a Point Charge So neutral objects are attracted by charges, but it is relatively small. The force falls of like 1 and α is typically very small. r 5 25/25