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)

Last Chapter: free space NOW: different materials 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 Depends on Frequency and Temperature… Boundary conditions Insulators (dielectrics) Conductors (metals) Semiconductors 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] 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. Doesn’t involve conductors, doesn’t satisfies 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 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 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)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I A Perfect conductor Has many charges that are free to move. Therefore it can’t 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)

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 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 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 Stroked by lightning NOTE: 0.1 A is enough to kill a person if not given immediate assistance 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 Cu is 1.81 x 1010C/m3.. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I PE 5.3 The free charge density in 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)

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

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 Boundary Conditions We have two materials How the fields behave @ interface? 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)

Cases for Boundary Conditions: Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Cases for Boundary Conditions: Dielectric- dielectric Conductor- Dielectric 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 c d D w Dh e1 E1t E2n e2 E2 E2t 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 Dh D S rS D1t e1 D2n D2 e2 D2t Electrical Engineering, UPRM (please print on BOTH sides of paper)

Conductor-dielectric B.C. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Conductor-dielectric B.C. Consider the figure below: En E q1 c d e1 Et dielectric conductor Dh s2=∞ E2=0 a b D w Electrical Engineering, UPRM (please print on BOTH sides of paper)

Conductor-dielectric B.C. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Conductor-dielectric B.C. Consider the figure below: En E q1 D S e1 Et dielectric conductor Dh rS s2=∞ E2=0 Electrical Engineering, UPRM (please print on BOTH sides of paper)

Summary B.C. Dielectric-dielectric Dielectric-conductor Because E=0 inside the conductor. Tangential Normal Tangential normal

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I PE 5.9 A homogeneous dielectric (er=2.5) fills region 1 (x<0), while region 2(x>0) is free space. Find Electrical Engineering, UPRM (please print on BOTH sides of paper)