1. Static Charges Matter carries electrical charges The charges arises from the presence of protons & electrons in the atoms that make up the matter & a force results between charged bodies The force on a static electrical charge are described by Coulombs Law- Where is the unit vector in the direction to q 1 from q 2 1/4  o =constant 10 -7 c 2 (or) 8.99  10 9 Nm 2 /coul 2 or Vm/coul Units of  o (permitivity of free space)=coul 2 /Nm 2 (or) coul/Vm

2. q 1 and q 2 are charges r is the distance between charges The forces can be :  attractive ( as in the case of a “+” and “-” charge) or  repulsive (as in the case of two “+” charges or two “-” charges) The most important charge in nature is that of an electron The charge on a electron is 1.60  10 -19 coulombs Static Charges

3. Electrical Fields If two charges are separated by a distance, r, charge 1 produces a “condition” at the location of charge 2 When a charge 2 is at the location, it ‘feels’ a force The condition is the electric field ‘E’ and is a vector in the direction of F and represents the force (in newtons) on a unit charge (C) at the point considered where r=r So, that the force at that location is: F=q 2  E Therefore: E=F/q 2

4. The formula shown before is for an electric field created by a single charge If a field is created by numbers of individual charges, the vector E fields from each charge need only be summed: E= E 1 + E 2 + E 3 +E 4 + … or Electrical Fields

5. Current The flow of electrical charge is defined as current Where I is in C/s= amperes (amps) One ampere is 1 C/s. Since the charge on an electron is 1.6022  10 -19 coulombs, it is equivalent to 6.2415  10 18 electrons passing a point in one second!

6. Electrostatic Potential (The Volt) A Volt (V) is the potential energy per unit charge The potential between two points is related to the work done in carrying a charge from a to b Since the electric field is force per unit charge, the work per unit charge (or potential) can be derived from: The unit for electrical potential is joule (work) per coulomb (unit charge) and is called volt This means that a charge of one coulomb (1 C) will acquire one joule (1 J) of energy falling through a potential difference of one (1 V)

7. Capacitance Capacitance is the ability to store charge. A capacitor usually consists of two conductors in a circuit separated by an insulator (dielectric). If a voltage is applied across the plates, excess charges will build up until the voltage is enough to discharge the capacitor across the dielectric The relationship of capacitance in a parallel plate: K-relative dielectric constant,  o -absolute permittivity, A - area of the plates, & d - distance separating the plates

8. In terms of applied voltage, capacitance can be described as: Q- the charge in coulombs V-potentials in volts C-capacitance in Farad Capacitance

9. It is defined as follows: Where I = Current (Ampere or C/s) V = Voltage (Volt or J/C) R = Resistance (Ohm or V/A) Ohm’s Law Electrical Conduction Resistance is a measure of resistance to flow of electricity. , resistance is in the units of volts per ampere. One volt per ampere is called an ohm (  ).

10. Can be expressed as Where J = Current density, A/m 2 E = Electric field, V/m ρ= electrical resistivity, Ωm Current Density Or Where Δq is the net quantity of charge flowing through an area A in time Δt

11. Resistivity (  ) Where l = distance between two points at which voltage is measured A = cross-sectioned area perpendicular to the direction of current  has the unit of  m Schematic representation of apparatus used to measure electrical resistivity

12. Electrical conductivity (  ) is the reciprocal of the resistivity (  )  has the unit of (  m) -1 solid materials show amazing range of conductivity over 27 orders of magnitude Using the conductivity : materials can be categorized: Metal-Good conductor Insulators-Very low conductivities Semiconductors-Intermediate conductivities

13. A conductor-a substance that allows current to flow through it A conductor-a substance that allows current to flow through it In metals, the current is composed of moving electrons In metals, the current is composed of moving electrons Electrolytic solutions also conduct current but by the movement or flow of ions Electrolytic solutions also conduct current but by the movement or flow of ions VS  Insulators have few mobile electrons or ions  The flow of current is inhibited  As fields are increased, dielectric breakdown of insulators occurs and the current is discharged as a surge  The dielectric strength is the maximum field an insulator can support

14. Conductors/Metals :  ~ 10 +7 (  m) -1 Semiconductors :  ~ 10 -6 to 10 +4 (  m) -1 Insulators :  ~ 10 -10 to 10 -20 (  m) -1

15. Most polymers and ionic ceramics are insulators with Eg > 2 eV Very small conductivity, then high resistivity  increases with temperature  Material Electrical Conductivity [(  -m) -1 ] Graphite10 5 CERAMICS Aluminum oxide Porcelain Soda-lime glass Mica 10 -10 - 10 -12 < 10 -10 10 -11 - 10 -15 POLYMERS Phenol-formaldehyde Nylon 6,6 Polymethyl methacrylate Polyethylene Polystyrene Polytetrafluoroethylene 10 -9 - 10 -10 10 -9 - 10 -12 < 10 -12 10 -13 - 10 -17 < 10 -14 < 10 -16 Electrical Conduction in Ionic Ceramics and in Polymers

16. Both cations and anions can move/migrate/diffuse under application of E Another definition of current- a net movement of these charged ions (in addition to electrons) Thus, conduction:  total =  electron +  ion Polymers are very insulative and mostly only electronic contribution Conducting Polymers (with dopants) Many applications due to low density, flexibility, and production ease Electrodes in rechargeable batteries Wiring in aircraft Electronic devices (Transistors/Diodes) Electrical Conduction in Ionic Materials and in Polymers

17. Electron Conduction in Real Mode Influence of Temperature Influence of Impurities Influence of Plastic Deformation

18.  Resistivity: Scattering of electrons due to crystal defects  Increasing the numbers of defect raises resistivity( lowers conductivity)  Number of defects depend on temperature, composition, specimen, and thermal history  total =  t +  i +  d  Matthiessen’s Rule  t = thermal contribution  i = impurity contribution  d = plastic deformation independent Electrical Resistivity of Metals

19. Influence of Temperature Temperature  o and a are constant for metal The temperature is dependent on thermal resistivity component on temperature is due to the increase with temperature in thermal vibrations and other lattices irregularities (i.e. vacancies) which serve as electron- scattering centers

21. Influence of Impurities Impurities For additions of a single impurity the impurity resistance  i is related to the impurity concentration c i in terms of the atom fraction (at 100%) A is a composition-independent constant that is a function of both impurity and host metals

23. ENERGY BAND A range of energies that electrons can have in a solid. In a single atom, electrons can exist in discrete energy levels. In a crystal, in which large numbers of atoms are held closely together in a lattice, electrons are influenced by a number of adjacent nuclei and the sharply defined levels of the atoms become bands of allowed energy; this approach to energy levels in solids is often known as the band theory. Each band represents a large number of allowed quantum states. Between the bands are forbidden bands. The outermost electrons of the atoms form the valence band. This is the band, of those occupied, that has the highest energy.

24. Conduction Band The band structure of solids accounts for their electrical properties. In order to move through the solid, the electrons have to change from one quantum state to another. This can only occur if there are empty quantum state to another. This can only occur if there are empty quantum states with the same energy. In general, if the valence band is full, electrons cannot change to new quantum states in the same band. For conduction to occur, the electron have to be in unfilled band - conduction band

25. Individual atom (Quantum Numbers : n, l, m, s) 1s 2s Bring 12 atoms closer Energy Band Structure in Solids

26.  At equilibrium spacing, band may not form in innermost electrons  Valence Band = the band that contains the highest energy or valence electrons Conduction Band = the next higher energy band, most likely unoccupied by electrons Energy Band Structure in Solids

27.  Fermi Energy E f = the energy of the highest filled state at 0 K  Valence band is partially filled (Cu) Filled valence band overlapping with conduction band (Mg) Filled valence band with “ energy band gap ” E g (insulator/semiconductors) Energy Band Structure in Solids

28.  Only electrons with E > E f are active in electric field   Hole = charged electronic entity with E < E f (found in insulators/semiconductors  Metal  metallic binding “electron gas”  vacant state next to E f  Easy to excite  high  Insulator  ionic/covalent bonding  highly localized e -  hard to move  large E g Semiconductor  weak covalent  Easy to move  low E g Atomic Bonding and Band Conduction

29. Ferroelectricity Exhibit spontaneous polarization which is polarization in the absence of electric field Materials exhibit ferroelectric properties: Barium Titanate, Rochelle salt, potassium dihydrogen phosphate, potassium niobate, lead zirconate-titanate Have extreme high dielectric constant at relatively low applied field frequencies Capacitors from this material much smaller than other dielectric materials

30. Piezoelectricity Pressure electricity Polarization is induced and electric field is established across a specimen by the application of external forces Utilized in transducers. For instance, some transducer will convert electrical energy into mechanical strains or vice versa Piezoelectric materials: titanates of barium & lead, lead zirconate, ammonium dihydrogen phosphate & quartz A common application of piezoelectric material -ultrasound transducer

31. From: http://www.pennhealth.com/ health_info/Surgery/ graphics/ultrasound_2.jpg From: http://static.howstuffworks.com/ gif/ultrasound1a.jpg