Electric fields in Material Space Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Electric fields in Material Space Sandra Cruz-Pol, Ph. D. INEL 4151 ch 5 Electromagnetics I ECE UPRM Mayagüez, PR Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Last Chapter: free space NOW: different materials Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Some applications Superconductors High permittivity dielectrics Transistors Electromagnets Electrical Engineering, UPRM (please print on BOTH sides of paper)

We will study Electric charges: Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I We will study Electric charges: Conductors or Insulators Depend on Frequency and Temperature… Boundary conditions Insulators (dielectrics) Conductors ~(metals) Semiconductors Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Material @ 20oC & Low frequency Conductivity [S/m] Silver 6.1 x 107 Copper 5.8 x 107 Gold 4.1 x 107 Aluminum 3.5 x 107 Carbon 3 x 104 Sea water 4 Silicon 4.4 x 10-4 Pure water 10-4 Dry Earth 10-5 Glass, Quartz 10-12, 10-17 Appendix B Conductors- have many free electrons available. Colder metals conduct better. (superconductivity) semiconductor Insulators at most lower frequencies. Electrical Engineering, UPRM (please print on BOTH sides of paper)

Current Units: Amperes [A] Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Current Units: Amperes [A] Definition: is the electric charge passing through an area per unit time. Current Density, [A/m2] Is the current thru a perpendicular surface: Electrical Engineering, UPRM (please print on BOTH sides of paper)

Depending on how I is produced: Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Depending on how I is produced: There are different types of currents. Convection- I flows thru isolator: liquid, gas, vacuum. Does not involve conductors, Does not satisfy Ohm’s Law Conduction- flows thru a conductor Displacement (ch9) Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Current in a filament u Convection current, [A] Convection density, A/m2 Dl DS rv Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Conduction Current Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Requires free electrons, it’s inside conductor. Suffers collisions, drifts from atom to atom Conduction current density is: Newton’s Law where rv=ne Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I A Perfect conductor Has many charges that are free to move. Therefore it cannot have an E field inside which would not let the charges move freely. So, inside a conductor: Charges move to the surface to make E=0 Electrical Engineering, UPRM (please print on BOTH sides of paper)

A typical lightning flash measures about 300 million volts and 30,000 amps Aug 22, 2015 http://www.hngn.com/articles/121982/20150822/lightning-bolt-strikes-delta-air-plane-bound-las-vegas-video.htm

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Resistance If you force a Voltage across a conductor: Then E is not 0 The e- encounter resistance to move E I rc S l V + - rc=1/s= resistivity of the material Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Power in Watts = Rate of change of energy or force x velocity F=QE Joule’s Law Electrical Engineering, UPRM (please print on BOTH sides of paper)

PE 5.1 Find the current thru the cylindrical surface Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I PE 5.1 Find the current thru the cylindrical surface For the current density Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I PE 5.2 In a Van de Graaff generator, w=0.1m, u=10m/s and the leakage paths have resistance 1014 W. If the belt carries charge 0.5 mC/m2, find the potential difference between the dome and the base. w= width of the belt u= speed of the belt Electrical Engineering, UPRM (please print on BOTH sides of paper)

PE 5.3 The free charge density in copper (Cu) is 1.81 x 1010C/m3.. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I PE 5.3 The free charge density in copper (Cu) is 1.81 x 1010C/m3.. For a current density of 8 x 106 A/m2, find the electric field intensity and the drift velocity. Electrical Engineering, UPRM (please print on BOTH sides of paper)

Polarization in dielectrics Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Polarization in dielectrics The effect of polarization on a dielectric is to have a surface bound charge of Qb and leave within it an accumulation of volume bound charge: rps and rpv are the polarization (bounded) surface and volume charge densities Electrical Engineering, UPRM (please print on BOTH sides of paper)

Permittivity and Strength Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Permittivity and Strength Not really a constant! Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dielectric properties Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Dielectric properties Linear = e doesn’t change with E Isotropic= e doesn’t change with direction Homogeneous= e doesn’t change from point to point. Coulomb’s Law for any material: Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I PE 5.6. A parallel plate capacitor with plate separation of 2mm has a 1kv voltage applied to its plane. If the space between its plates is filled with polystyrene, find E and P. Electrical Engineering, UPRM (please print on BOTH sides of paper)

PE 5.7.In a dielectric material, Ex= 5V/m and Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I PE 5.7.In a dielectric material, Ex= 5V/m and Find: Electrical Engineering, UPRM (please print on BOTH sides of paper)

5. 13 In a slab of dielectric material for which e = 2 5.13 In a slab of dielectric material for which e = 2.4eo and V=300z2 V, Find (a) D and rv (b) P

Extra slides Not to be covered in this course

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Continuity Equation Charge is conserved. Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I For steady currents: Change= output current –input current = 0 Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Boundary Conditions We have two materials How do the fields behave @ interface? We look at the tangential and the perpendicular component of the fields. Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dielectric-dielectric B.C. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Dielectric-dielectric B.C. Consider the figure below: E1n E1 q1 a b e1 E1t Dh E2n e2 E2 c d E2t D w Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dielectric-dielectric B.C. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Dielectric-dielectric B.C. Consider the figure below: D1n D1 D S D1t e1 Dh rS D2n D2 e2 D2t Electrical Engineering, UPRM (please print on BOTH sides of paper)