We will study Electric charges: Some applications. NOW: different materials. Dr. S. Cruz-Pol, INEL Electromagnetics I

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Dr.. Cruz-Po, INL 4151- ectric fieds i Materia pace adra Cruz-Po, Ph. D.

materias ome appicatios upercoductors High permittiity dieectrics Trasistors

Frequecy ad Temperature Boudary coditios Coductors ~(metas) Isuators

6.1 7" Copper 5.8 7 " God 4.1 7" Aumium 3.5 7" Carbo 3 4" ea water 4" iico 4.

Coductorshae may free eectros aaiabe. Coder metas coduct better.

Curret Uits: Amperes [A] Defiitio: is the eectric charge passig through a

1 Dr.. Cruz-Po, INL ectric fieds i Materia pace adra Cruz-Po, Ph. D. INL 4151 ch 5 C UPRM Mayagüez, PR Last Chapter: free space NOW: differet materias ome appicatios upercoductors High permittiity dieectrics Trasistors ectromagets We wi study ectric charges: Coductors or Isuators o Deped o Frequecy ad Temperature Boudary coditios Coductors ~(metas) Isuators (dieectrics) emicoductors 0 o C & Low frequecy Coductiity [/m] ier 6.1 7" Copper " God 4.1 7" Aumium 3.5 7" Carbo 3 4" ea water 4" iico 4.4-4" Pure water -4 " Dry arth -5 " Gass, Quartz -1, -17" Appedi B Coductorshae may free eectros aaiabe. Coder metas coduct better. (supercoductiity) semicoductor Isuators at most ower frequecies. Curret Uits: Amperes [A] Defiitio: is the eectric charge passig through a area per uit time. dq I Curret Desity, [A/m ] Is the curret thru a perpedicuar surface: J I J d ΔI Δ o BOTH sides of paper) 1

Dr.. Cruz-Po, INL 4151- Depedig o how I is produced: There are differet types of currets. Coectio- I fows thru isoator: iquid, gas, acuum.

2 Dr.. Cruz-Po, INL Depedig o how I is produced: There are differet types of currets. Coectio- I fows thru isoator: iquid, gas, acuum. o Does ot ioe coductors, o Does ot satisfy Ohm s Law Coductio- fows thru a coductor Dispacemet (ch9) Curret i a fiamet Coectio curret, [A] ΔQ ρ ΔΔ I ρδu Δt Δt Coectio desity, A/m Δ ΔI J ρu Δ u ρ Δ Coductio Curret F e Requires free eectros, it s iside coductor. uffers coisios, drifts from atom to atom m mass of eectro mu e τ time betwee coisios τ u drift eocity Newto s Law Coductio curret desity is: e τ J ρ u σ m where ρ e A Perfect coductor Has may charges that are free to moe. Therefore it caot hae a fied iside which woud ot et the charges moe freey. o, iside a coductor: 0 ρ 0 V Charges moe to the surface to make 0 ab 0 Resistace If you force a Votage across a coductor: The is ot 0 The e- ecouter resistace to moe Aug, 015 I V / J I / σ R V I σ ρ c + - V ρ c 1/σ resistiity of the materia o BOTH sides of paper)

Dr.. Cruz-Po, INL 4151- Power i WaDs Rate of chage of eergy or force eocity ρd u ρud P Jd P d Jd L P VI Joue s Law P 5.

1m, um/s ad the eakage paths hae resistace 14 Ω. If the bet carries charge 0.5 µc/m, fid the potetia differece betwee the dome ad the base. w wih of the bet u speed of the bet I ρ uw 0.5 6 ()(.

3 Dr.. Cruz-Po, INL Power i WaDs Rate of chage of eergy or force eocity ρd u ρud P Jd P d Jd L P VI Joue s Law P 5.1 Fid the curret thru the ρ cyidrica,1 z 5m surface J zsi φ â ρ [ma / m ] For the curret desity I J d z dz si φ ρ ρ dφ 5 1 π (5 1) φ si φ I 0 4 I 40π 0 754mA π 0 P 5. I a Va de Graaff geerator, w0.1m, um/s ad the eakage paths hae resistace 14 Ω. If the bet carries charge 0.5 µc/m, fid the potetia differece betwee the dome ad the base. w wih of the bet u speed of the bet I ρ uw ()(.1) 6 14 V IR (.5) ( ) 50MV P 5.3 The free charge desity i copper (Cu) is 1.81 C/m 3.. For a curret desity of 8 6 A/m, fid the eectric fied itesity ad the drift eocity. 6 J u ρ 1.81 J ρ u σ 6 J 8.138V / m σ m / s Poarizatio i dieectrics The effect of poarizatio o a dieectric is to hae a surface boud charge of: ad eae withi it a accumuatio of oume boud charge: Qb ρ pd D o + P P χe o ρ ps P aˆ ρ P p ρ ps ad ρ p are the poarizatio (bouded) surface ad oume charge desities o BOTH sides of paper) 3

Dr.. Cruz-Po, INL 4151- PermiDiity ad tregth Not reay a costat D o + P o + χ e o o r r 1+ χe o Dieectric properties Liear does t chage with Isotropic does t chage with directio Homogeeous does t

4 Dr.. Cruz-Po, INL PermiDiity ad tregth Not reay a costat D o + P o + χ e o o r r 1+ χe o Dieectric properties Liear does t chage with Isotropic does t chage with directio Homogeeous does t chage from poit to poit. Couomb s Law for ay materia: F Q Q 4π o r R 1 1 aˆ 1 P 5.6. A parae pate capacitor with pate separatio of mm has a 1k otage appied to its pae. If the space betwee its pates is fied with poystyree, fid ad P. r.55 V kaˆ V / m d.00 χ e r P χ e o (1.55)( ) â µc / m P 5.7. I a dieectric materia, 5V/m ad P 1 ( )C / m π 3â â + 4â y z Fid: χ e,, ad D P P oχe χe.16 o P 5 aˆ 1.67aˆ y aˆ z oχe rp D o r 140 aˆ 477aˆ y + 186aˆ z χ e Questios? Charge is cosered. Cotiuity quatio I I out J d J d i dq d dρ J ρ d o BOTH sides of paper) 4

5 Dr.. Cruz-Po, INL For steady currets: Boudary Coditios Chage output curret iput curret 0 dρ 0 J 0 We hae two materias How do the fieds iterface? auate Mawe' s : d 0 t + D d Q We ook at the tagetia ad the perpedicuar compoet of the fieds. ec Dieectric-dieectric B.C. Cosider the figure beow: 1 1 θ 1 t 1 1t d 0 0 Δw d a 1t 1 Δ w 1 1 t t t cotiuous t 1 tδw + c b D1 t Dt discotiuous D Dieectric-dieectric B.C. Cosider the figure beow: D 1 D 1 if o free charges : D 1t 1 D D is cotiuous. D t 1 D ΔQ ρ Δ D Δ D Δ 1 1 D Δ D ρ s ρ s D d if o free charges : I a sab of dieetric materia for which.4 o ad V300z V, Fid V (a) D ad ρ (b) P V V â + ây + y z âz 600z â z V D.4 o 1.7zC / m ẑ ρ D 1.7C / m 3 P o χ e (1.4)o ( 600z)ẑ 7.43zC / m ẑ o BOTH sides of paper) 5

Chapter 2 Motion and Recombination of Electrons and Holes

Chapter 2 Motion and Recombination of Electrons and Holes Chapter 2 Motio ad Recombiatio of Electros ad Holes 2.1 Thermal Eergy ad Thermal Velocity Average electro or hole kietic eergy 3 2 kt 1 2 2 mv th v th 3kT m eff 3 23 1.38 10 JK 0.26 9.1 10 1 31 300 kg