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

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Last Chapter: free space NOW: different materials

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Some applications superconductors High permittivity dielectrics Transistors Electromagnets

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We will study Electric charges: Conductors or Insulators Depends on Frequency and Temperature… Boundary conditions Conductors (metals) Insulators (dielectrics) Semiconductors

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Current Units: Amperes [A] Definition: is the electric charge passing through an area per unit time. Current Density, [A/m 2 ] The current thru a perpendicular surface:

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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)

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Current in a filament Convection current, [A] Convection density, A/m 2 SS vv u ll

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Conduction Current Requires free electrons, it’s inside conductor. Suffers collisions, drifts from atom to atom Conduction current density is: Newton’s Law where v = ne

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Material @ 20 o C Low frequency Conductivity (S/m) Silver6.1 x 10 7 Copper5.8 x 10 7 Gold4.1 x 10 7 Aluminum3.5 x 10 7 Carbon3 x 10 4 Sea water4 Silicon4.4 x 10 -4 Pure water10 -4 Dry Earth10 -5 Glass, Quartz10 -12, 10 -17 Colder metals conduct better. (superconductivity) Insulators at most lower frequencies. Conductors- have many free electrons available. semiconductor Appendix B

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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

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Resistance If you force a Voltage across a conductor: Then E is not 0 The e- encounter resistance to move I E V + - S l c = resistivity of the material

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

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PE 5.1 Find the current thru the cylindrical surface For the current density NOTE: 0.1 A is enough to kill a person if not given immediate assistance Stroked by lightning

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PE 5.2 In a Van de Graaff generator, w=0.1m, u=10m/s and the leakage paths have resistance 10 14 . If the belt carries charge 0.5 C/m 2, find the potential difference between the dome and the base. w= width of the belt u= speed of the belt

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PE 5.3 The free charge density in Cu is 1.81 x 10 10 C/m 3.. For a current density of 8 x 10 6 A/m 2, find the electric field intensity and the drift velocity.

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Permittivity Not really a constant!

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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.

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Continuity Equation Charge is conserved.

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

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

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Cases for Boundary Conditions: 1.Dielectric- dielectric 2.Conductor- Dielectric

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Dielectric-dielectric B.C. Consider the figure below: E1E1 E2E2 E 1t E 1n E 2t E 2n ab c d w hh 11 22 11

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Dielectric-dielectric B.C. Consider the figure below: D1D1 D2D2 D 1t D 1n D 2t D 2n 22 11 hh S SS

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Conductor-dielectric B.C. Consider the figure below: E EtEt EnEn a b c d w hh 11 2 =∞ E 2 =0 11 dielectric conductor

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Conductor-dielectric B.C. Consider the figure below: E EtEt EnEn hh 11 2 =∞ E 2 =0 11 dielectric conductor S SS

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

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PE 5.9 A homogeneous dielectric ( r =2.5) fills region 1 ( x 0) is free space. Find

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