Chapter 15 Matter and Electric Fields

Question 1 (Chap. 14) What is the direction of the electric field at location X, due to the dipole? - + C B D X Answer: B E A

Question 2 (Chap. 14) Locations 1 and 2 are equidistant from the center of the dipole. At which location is the magnitude of the electric field larger? at location 1 at location 2 magnitudes are the same d - + 1 d Answer: A 2

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

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 If we remove all electrons from human body charge will be 70kg/1.7e-27kg*1.6e-19C=6.6e9 C, 6 billion Coulomb. If you and I are separated by the Earth-moon distance of 4 x 10^8 m, Force = 9e9*(6.6e9)^2/16e16 = 2.4e12 N Ordinary matter is electrically neutral. However, can be charged by adding/removing charged particles Can we create an excess charge inside a sample?

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. Example: when you comb your hair the comb gets charged and so does your hair, the magnitude is equal, sign is different.

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

Polarization Amount of polarization p in most materials is proportional to 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.

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

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

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

A Neutral Atom and a Point Charge 1) 3) 2) 4. Induced dipole exerts force F1 on the charge: 1/r^5 because induced p proportional to 1/r^2 and it produces a field at q1 proportional to p/r^3.

A Neutral Atom and a Point Charge 1) 3) 2) 4) 5. The charge q1 exerts force F2 on the dipole (reciprocity):

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

Exercise Atom A is easier to polarize than atom B. Which atom would experience a greater attraction to a point charge a distance r away? + - FA FB A + - B

Conductors and Insulators Different materials respond differently to electric field Conductor: contains mobile charges that can move through material Insulator: contains no mobile charges All materials are made of atoms that contain electrons and protons, but different materials respond in different ways to electric fields. Insulator: electrons are tightly bound to the molecules Conductors: free moving charged particles

Polarization of Insulators Insulator: Electrons are bound to the atoms or molecules. Electrons can shift slightly (<1 Å), but remain bound to the molecule. Individual atoms or molecules can be polarized by external electric field. We have seen that an individual atom or molecule can be polarized by an applied electric field, producing an induced dipole of atomic or molecular dimension. No charged particles can move more than 10-10 m There are a lot of molecules – the net effect produced by the induced dipoles can be very large.

Polarization of Insulators Diagram showing polarization of an insulator: Dipoles: exaggerated in size; stretch: degree of polarization No mobile charges: excess charges stay where they are Electrons remain bound to the molecule

Low Density Approximation Field E at a location of a molecule is a superposition of the external applied field and the field created by other induced dipoles: What happens if we apply an electric field to an insulator? No mobile charges in an insulator, excess charges stay where they are. Simplifying assumption:

Conductors There are charges which can move freely throughout the material E In contrast to an insulator, where electrons and nuclei can move only very small distances, the charged particles in a conductor are free to move large distances. Polarization of conductors differs from that of insulators.

Ionic Solutions are Conductors (home) Salt water: Na+ and Cl- H+ and OH- Apply external electric field When an electric filed is applied to a conductor, the mobile charged particles begin to move in the direction of the force exerted on them by the field. As the charges move, they begin to pile up in one location, creating a concentration of charge  creates electric field. The net electric field is the superposition of the applied field and field created by the relocated charges. Example: Sodium chloride : sodium ions and chloride ions When electric field is applied: Put electrodes in – field at all times, no static equilibrium.

Ionic Solutions are Conductors (home) Assumption: charges will move until Enet=0 (static equilibrium) Proof: by contradiction: Assume Enet≠0 Mobile ions will move This is not equilibrium Assumption Enet≠0 is wrong Polarization occurs very rapidly but it is not instantaneous (10-18 s). Only few ions move and only short distances until equilibrium is reached! Put electrodes in – field at all times, no static equilibrium. Enet=0 It is not a shielding effect, but a consequence of superposition!

A Model of a Metal Positive atomic cores Metal lattice and mobile-electron sea Metal lattice Electrons are not completely free – they are bound to the metal as a whole. There is no net interaction between mobile electrons

Drude Model of Electron Motion in a Metal - No net interaction between mobile electrons Forget previous velocity after collision Later we will show that conductivity ()  μ Some important sources of collision: - impurities - thermal motion of atoms (more motion at higher temperature T  shorter  lower  [common feature of metals]) (mobility)

Metal in Electric Field Enet inside the conductor will be: A. Uniform positive B. Uniform negative C. Zero D. will have complex pattern Metal polarizes! Polarized is nor equal to charged

Metal in Electric Field Metal polarizes! Polarized is nor equal to charged Note: It is not charged! Net charge is still zero Simplified diagram of polarized metal