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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 spaceNOW: different materials

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

  4. We will study Electric charges: • Conductors or Insulators • Depends 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. • Doesn’t involve conductors, • doesn’t satisfies Ohm’s Law • Conduction- flows thru a conductor • Displacement (ch9)

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

  11. 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

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

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

  14. 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

  15. 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.

  16. Polarization in dielectrics The effect of polarization on a dielectric is to have a surface bound charge of: and leave within it an accumulation of volume bound charge: rpsand rpvare the polarization (bounded) surface and volume charge densities

  17. Permittivity and Strength • Not really a constant!

  18. 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:

  19. 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.

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

  21. Continuity Equation • Charge is conserved.

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

  23. Substituting in: where Tr=e/s is called the Relaxation time

  24. What is Relaxation Time? [s]

  25. What is Relaxation Time? [s] Is the time it takes a charge placed in the interior of a material to drop to e-1 of its initial value. • Find Tr for silver • Find Trfor rubber:

  26. Boundary Conditions • We have two materials • How the fields behave @ interface?

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

  28. Cases for Boundary Conditions: • Dielectric- dielectric • Conductor- Dielectric • Conductor-Free Space

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

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

  31. Dielectric-Dielectric B.C. In summary: E1n E1 q1 Dh E1t e1 D2n e2 D2 D2t

  32. Conductor-dielectric B.C. • Consider the figure below: En E c q1 d e1 Et Dh dielectric conductor s2=∞ E2=0 a b D w

  33. Conductor-dielectric B.C. • Consider the figure below: En E D S q1 e1 Et Dh dielectric conductor rS s2=∞ E2=0

  34. Conductor-Free Space B.C. • Consider the figure below: En E c q1 d eo Et Dh Free space conductor s2=∞ E2=0 a b D w

  35. PE 5.9 A homogeneous dielectric (er=2.5) fills region 1 (x<0), while region 2(x>0) is free space. • Find

  36. 5.29 Lightning strikes a dielectric sphere of radius 2-mm for which er=2.5, s=5x10-6 S/m and deposits uniformly a charge of 1C. • Determine the initial volume charge density and the volume charge density 2ms later. Answer: 29.84KC/m3, 18.98 kC/m3

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