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Understanding Electric Fields in Different Materials: Applications and Concepts

Explore the intricacies of electric fields in various materials, including superconductors, dielectrics, transistors, and more. Learn about electric charges in conductors, insulators, and semiconductors, and delve into current densities, resistances, and polarization effects.

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Understanding Electric Fields in Different Materials: Applications and Concepts

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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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