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Electric fields in Material Space

Electric fields in Material Space. Sandra Cruz-Pol, Ph. D. INEL 4151 ch 5 Electromagnetics I ECE UPRM Mayagüez, PR. Last Chapter:. free space. NOW: different materials. Some applications. Superconductors High permittivity dielectrics Transistors Electromagnets.

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Electric fields in Material Space

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  1. Electric fields in Material Space Sandra Cruz-Pol, Ph. D. INEL 4151 ch 5 Electromagnetics I ECE UPRM Mayagüez, PR

  2. Last Chapter: free space NOW: different materials

  3. Some applications • Superconductors • High permittivity dielectrics • Transistors • Electromagnets

  4. We will study Electric charges: • Conductors or Insulators • Depend on Frequency and Temperature… • Boundary conditions Insulators (dielectrics) Conductors ~(metals) Semiconductors

  5. Appendix B Conductors- have many free electrons available. Colder metals conduct better. (superconductivity) semiconductor Insulators at most lower frequencies.

  6. CurrentUnits: 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:

  7. 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)

  8. Convection current, [A] Convection density, A/m2 Current in a filament u Dl DS rv

  9. 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

  10. 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

  11. 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

  12. 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

  13. Joule’s Law Power in Watts = Rate of change of energy or force x velocity F=QE

  14. PE 5.1 Find the current thru the cylindrical surface • For the current density

  15. PE 5.2 In a Van de Graaff generator, w=0.1m, u=10m/s and the leakage paths have resistance 1014W. • 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

  16. 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.

  17. 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: Polarization in dielectrics rpsand rpvare the polarization (bounded) surface and volume charge densities

  18. Permittivity and Strength • Not really a constant!

  19. 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:

  20. 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.

  21. PE 5.7.In a dielectric material, Ex= 5V/m and • Find:

  22. 5.13 In a slab of dielectric material for which e = 2.4eo and V=300z2V, Find(a) D and rv (b) P

  23. Extra slidesNot to be covered in this course

  24. Continuity Equation • Charge is conserved.

  25. For steady currents: • Change= output current –input current = 0

  26. Boundary Conditions • We have two materials • How do the fields behave @ interface? We look at the tangential and the perpendicular component of the fields.

  27. Dielectric-dielectric B.C. • Consider the figure below: E1n E1 q1 a b e1 E1t Dh E2n e2 E2 c d E2t D w

  28. Dielectric-dielectric B.C. • Consider the figure below: D1n D1 D S Dh e1 D1t rS D2n e2 D2 D2t

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