# Electric fields in Material Space

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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
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 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 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 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)