Physics 272: Electricity and Magnetism. Mark Palenik Thursday June 14 th

Transcription

1 Physics 272: Electricity and Magnetism Mark Palenik Thursday June 14 th

2 Topics Finish up dipoles Polarization of materials Conductors Charging/discharging

3 iclicker (not credit) An atom is placed in a UNIFORM electric field pointing to the right and polarizes. What is the net force on the atom? E a) To the left b) To the right c) No net force

4 Force on a dipole (clicker, no credit) Net force on a dipole = Force on positive charge + Force on negative charge F net = F pos +F neg = qe pos qe neg = q E pos E neg Assume we have a permanent dipole (not induced by an external electric field) In which situation could this force be non-zero? a) It is placed in a uniform field E b) A charge is placed along the perpendicular axis c) A charge is placed along the parallel axis + d) Either b) or c) +

5 Force on a point dipole We saidf net = q E pos E neg For a point dipole, P (dipole moment) is important, q is meaningless Charges are distance s apart P F net = lim E P s 0 s pos E neg = lim E(x + s) E(x) = s 0 s E(x+s) E(x) P lim s 0 s What does this look like? (think calculus) It s a derivative! dy dx s - + x x+s y x+h y(x) = h

6 Dipoles respond to E field derivatives Force on a dipole = Dipole moment * Derivitive of E field along dipole axis. E.g. if dipole is along x axis F net = P de dx More formally we could write F net = P E Tensor

7 Polarization of materials Recall: Electric field lines push on positive charges and pull negative charges Neutral atoms will polarize under the influence of electric fields Materials are made of atoms, so materials will polarize We call this INDUCED polarization Conductors and insulators behave differently

8 Electric fields and materials Plastic is an insulator: charges are not free to flow E E Plastic sphere: each atom becomes polarized, since the electrons cannot flow Metals are conductors E E=0 Metal sphere, electrons can flow. Sphere polarizes. Protons DO NOT move

9 Polarization of a plastic sphere Draw the E field lines from the positive charge and the polarization of this plastic sphere. Remember two things: 1) electrons are pushed opposite to the direction of field lines 2) The field lines are NOT horizontal + Plastic Sphere

10 Non-external electric field The external electric field acting on a plastic sphere is drawn below. Draw the electric field produced by the induced dipoles below E Note the field outside the sphere does not oppose the applied E The field of the induced dipoles inside the sphere opposes the applied field. As we will see, conductors are a special case.

11 Net field Superposition still applies One part of the field comes from the external, applied field Another comes from the polarization field E net = E ext + E pol E pol is induced by the external field. This happens in both conductors and insulators

12 Clicker Question A x + - B D Plastic Block C What is the direction of the electric field at X due to the dipole?

13 Clicker Question A x + - B D Plastic Block C What is the direction of the electric field at X due to the plastic box?

14 Clicker Question A x + - B D Plastic Block C What is the direction of the NET electric field at X?

15 Electric fields and metals Electrons are free to move inside of metals (nuclei are still fixed, i.e. the atoms don t move) What happens if I apply an external field to a piece of metal? Will the electrons move? Will they ever stop moving? If so, when?

16 Electric field in a conductor At equilibrium, E inside any conductor is zero Equilibrium is defined as when charges are static If there is an E field, the charges will move Therefore, in equilibrium, E=0 throughout the conductor Charges arrange themselves so that they cancel the external E field Reasons charges stop a) E pushes charges toward equilibrium b) Friction like forces slow electrons E E net =0 The electric field produced by the sphere with this arrangement of charges points left Applied field points to the right. The external applied field and field produced by the sphere cancel each other inside.

17 iclicker question: non-spherical conductor Which best describes the NET electric field inside of this triangular conductor with a positive charge nearby Metal triangle + a) It points to the right, because of the positive charge b) Non-zero because the conductor is not spherical, but not necessarily to the right c) Zero, because the triangle is a conductor d) It points toward the positive charge

18 Charged conductor Where will excess charges go if I put them on a conductor? Keep in mind how charges affect each other In inject several positive charges into the center of a metal sphere, so it is no longer neutral. Where do they go? When is the sphere in equilibrium?

19 Charged conductor and external charge Qualitatively describe the net field of a charged, conducting sphere and a point charge Point charge - Conducting sphere Recall the field outside a uniformly charged sphere is the same as that of a point charge? Is the total field the same as the sum of the field of the individual objects? In what circumstances might this or might this not be true?

20 Discharging by contact On approach: body polarizes On contact: charge redistributes over larger surface

21 Charging by induction

22 What is a conductor? Charges in conductors can be mobile. Either electrons or ions can flow In metals, there is a well ordered crystal structure, many close energy levels: a sea of electrons that can flow Gray is the electron sea. The red + s are the positive cores

23 What is a conductor 2 In ionic solutions, molecules have split into + and ions, which can flow in solution. E.g. NaCl becomes Na+ and Cl-