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# 90 Class Note for ECE 20100 at Purdue

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COURSE
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TYPE
Class Notes
PAGES
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WORDS
KARMA
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This 9 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Purdue University taught by a professor in Fall. Since its upload, it has received 20 views.

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Date Created: 02/06/15
10 ECE 201H POTENTIALLY USEFUL FORMULAS A Electrostatics Force felt by a charge q inside a static electric eld FqE Gauss s law in free space Q enc Electrostatic elds are conservative EXE0 Edl0 C Electric eld produced by a single static charge q in free space a q 7 PU E 3 4713980 R 7 Electric eld 7 voltage relationships 4 a P2 a a E7VV V27V17 El P1 Voltage produced by a single static charge q in free space V 4m R 7 Pa Equivalent polarization charge densities sz 13 pps13d n Electric Displacement D60E13 If a material is linear7 isotropic and homogeneous7 I3 soxgE and D 63er 5E Ohm s law 11 Continuity of charge a Vf7 12 Total electrostatic energy stored in a volume V 1 2 V 13 Total power dissipated in a volume V electrostatics PE fdv V We Some Useful Vector Identities ABXCBCxACAXB AxBxCBAC CA39B VipV1VV Vth V A39 VAAV Vx A VxAV xA VAxBBVxA AVXB VVVV2V 39VxVxAVVA VZA VxVV0 VVxAO VV A do i A 39 ds Divergence theorem L V x A ds 9QCA d6 Stokes s theorem Gradient Divergence Curl and Laplacian Operations Cartesian Coordinates x y z 0V 6V 6V VV a ay az ax 0y az an 8A 6A V A Z Z 6x 6y az ax 3y az AX Ay AZ 62V 62V 62V VZV 7 quot7 2 6x 6y az Av A 6A T M aAI A i 6 2 tax aAa m a zaz y 6x By 62 6y az 39 a 6x 6x 6y gt IGI 645L OJegp644 I eq 5 Witxiq fiV 660 644 Reqigt soili39lums MI gt Mrer 52 vnxi svaeqierhM sr XlijvsrxtekiSRP 2 62 Wls 511p syv svo jsvxli jsgs mck tvsfpiq wws Xlex tempgihmc ger fi ewukrih2 Gvsvm syxgplevg er svo lngl nwxs fi hmzikevhih2 F i gi39xmem Xlexxli em ivnwhmmrkyrmlefp jvsq Xli SD2Y rwyttsvxih em ivw Imvrsx fi knzir gvihnx yrplvm sxliv nwi mchnge h2 72 Q eoi syvem ivggevojsvieq tp390ft1Egnfkmmf e fs2 82 I xve tetivnwezengafp39 nj riihih2 F i wyvi xs pafipxli tvsfpiq ryq fivjsviegl teki sj syv SVOZ 92 Ywi yrmM livi viuynvih2 2 F i wyvi Xlex syv SVOO erh hnwgywmsrw erh i tpErexnsrw lir viuyimdhOevi gpevOgsrgmvio erh svkermih2 7 Useful vector identities differential elements and constants and physical relations are given exxli feg ijli I eq2 lt2 Xli tsrctthmmfyxmsr sr Xlnwieq nweszgs wgt Tvsfpiq EFIX swgsqi Tsmrxu 5 m 74 6 m 64 7 m 54 8 m 54 9 m 59 m 59 EFIX Wgsvi Viwypc m 3544 iw 3 rs 52 74 tmlz Jsviegl ijli jsgs ruck uyiwmrwotpewi erw ivm 516 pcriwmhcrk xs fi eweggyve erh gsrgnwi m syv i tperexnsrw erh gegypamsrw ew t swmprZ a 5 pts A capacitor has 10 p0 stored charge and 10 ml stored energy Please nd its geteguergiZ C 1 L WL V1 Qza u gi E Lf103p 2 2C 2W 1NDquot b 5 pts Please make a two dimensional sketch of the electric eld lines and equipotential Wjegiw sj er ipigmng hntsp392 syvvobigl wlsypn fi eweggy39ve ewtswmfp g 9 tmlz Ng39xli ipigmng tsxinmpnwivs exe tsrctxm vtegiOhsiwmcjng Xlexxli ipngrg eld is also zero at this point as well Please explain No LI 5 Vlo a w E39s 3v awn Hawth 44W Vollose wuay lac um qJ o rainF smaw 4w crm ah at 7 This 31 tcng39n39wl by Jhe cpowurrlc iv d 5 pts Please de ne mobility of the electrons in a conductor 1 he 311m 4 44mm man 1H 11 41 nf M an Weed am til6W5 39nn H c onAHt lw M Ma dgc39l39vlz lwl39cle il Hunt 423M 0 4 e 5 pts Please state Kirchhoff s voltage law in words The AleLVN w u all willquot 395 3 quot7 439quot 4 bahtw j 9 tmE lex hs i q ier f weka Xlexe hnipgmrgq e vvepnwmsmstrgc Krrzi leii ieq tp39w sj hnipigwrgnl exger fi ywyegj gsmmivjh msth lgolrgf g 7 u q ulnar and la l39 a wurlrlg lc 0quot 5 Cadnu PK qn By Mary 97 641 HexMFA H l 39 mad 62 64tm12 Gsrwfnive tevemptpzm39 getegusv nxl tpaxi evie E Otpaxi Mtevexmr h erh jvii space between the plates Ignoring fringing eld please prove that the capacitance of the getegmltsvan A amp4EAh Note if you know the eld produced by an in nite charged plate sy ger ywi nxm syv svo mdsyxtvszmck m2 SOQJULHDV in HM no k4 72 54tm12 G srwmive q ihnyq nxl gsrwexxgsrhygmmc 0392 Tvszi XlexV X MA 4 iziv livi rcrxliqihnqu J 4 We mow ko a Vx5o Sinu JrE 14 quot 9 a 0 and 539 ch r is uni914 Vvlt a a J 6x3 9 9 7x7 0 b 82 54 tmlz E zsgq i glevki hmmmfymsr pz A 9 rGAq 7 exists in the region de ned as 4 S S 60 5 S S 704 S S 82Tpewi gegypaxi Xli xsxepglevki m X1ivikm3r2 L 3 1 lsSPan SJXaigJy 1j2JE V o O 3 wt S12f 17 9 5 15 pts In a dielectric material the relationship between the ux density Pf and electric eld 1 nwkrrzir fgt MAegqfpr livi p erh F evi e gsrwxexx vgepev erh zigxsvvivtigmiQZ Jmch Xli tsrevmemsr sj Xlnw hriggmng ewe jyrgmsr sj SqOI39OM erh 172 W L B J D 39 39 P2toEI413 same 1339 2aEpa of 2 59 tmlz Gsrxmhiv X 5 mg tpi hniggxmgwE erh F2Xli igngng Witxfmnx sj q egtdwepE is three tim larger than the electric susceptibility of material B If the electric ux density is the same in both materials nd the relationship between the polarizations in materials A erh F m sxliv svthi tviwu TE ewe jyrgxmsr sj TF 2 7k 37 s 9 v a F a r Finec DA93 agtE9EAA oEB39Puu7 t 399 39 LEA 53 EA EEg 2ng 39 9 quot l W 39 HM 1 Q hz Es gt Ea B 58 299 Th i33ka 5 31 28 El

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