Home Explore TYT AYT 11. Sınıf Fizik Ders İşleyiş Modülleri Modül 5 Elektriksel Kuvvet ve Elektrik Alan Elektriksel Potansiyel Düzgün Elektrik Alan ve Sığa

TYT AYT 11. Sınıf Fizik Ders İşleyiş Modülleri Modül 5 Elektriksel Kuvvet ve Elektrik Alan Elektriksel Potansiyel Düzgün Elektrik Alan ve Sığa

Published by Nesibe Aydın Eğitim Kurumları, 2019-08-29 01:01:31

Description: TYT AYT 11. Sınıf Fizik Ders İşleyiş Modülleri Modül 5 Elektriksel Kuvvet ve Elektrik Alan Elektriksel Potansiyel Düzgün Elektrik Alan ve Sığa

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www.aydinyayinlari.com.tr 11. SINIF 5. MODÜL ELEKTRİKSEL KUVVET VE ELEKTRİK ALAN ELEKTRİKSEL POTANSİYEL DÜZGÜN ELEKTRİK ALAN VE SIĞA ELEKTRİKSEL KUVVET VE ELEKTRİK ALAN ³ Elektrostatik t 2 ³ Elektriksel Kuvvet t 6 ³ Çok Sayıda Yükün Coulomb Kuvveti t 7 ³ Elektriksel Alan t 11 ³ Elektrik Alan Kuvvet Çizgileri t 12 ³ Konu Testleri t 15 ³ Karma Testler t 17 ³ Yazılı Soruları t 21 ³ Yeni Nesil Sorular t 23 1

KONUYA HAZIRLIK #VTBZGBEBLJJÀFSJLi&MFLUSJLTFM,VWWFUWF&MFLUSJL\"MBOuLPOVTVZMBJMHJMJTOGUBHÌSEÑôÑOÑ[LPOVMBSOUFLSBSBNBDZMBIB[SMBONöUS Elektriksel Kuvvet ve Elektrik Alan ÷MJöLJMJ,B[BONMBS 9.6.1.1. : &MFLUSJLMFZÐLMFONF¿FõJUMFSJOJËSOFLMFSMFB¿LMBS 9.6.1.2. : &MFLUSJLMFOFOJMFULFOWFZBMULBONBEEFMFSEFZÐLEBóMNMBSOLBSõMBõUSS %PLVONBJMF&MFLUSJLMFONF + /ËUS :ÐLMÐCJSDJTJNJ¿JCPõJMFULFOLÐ- + + Nötr ve iletken bir cisim yüklü ve iletken bir cisme do- r1 ++ + + SFZF EõUBO EPLVOEVSVMVSTB UPQ- LVOEVSVMVSTB BSBMBSOEB ZÐL QBZMBõN PMVS :ÐL BLõ + MBN ZÐLÐ ZBS¿BQMBSZMB EPóSV DJTJNMFS PSUBL CJS FMFLUSJLTFM QPUBOTJZFMF VMBõODBZB LB- r2 EBSEFWBNFEFS + + + + PSBOUMPMBSBLQBZMBõSMBS :ÐLMFSJRKWFRL ZBS¿BQMBSSK ve rL olan iletken K ve ++ mmmmmmm m m m m mm mm mmmmmm - LÐSFMFSJ ZBMULBO TBQMBSOEBO UVUVMBSBL CJSCJSJOF EP- ++ m mmm mmm mm mm m m LVOEVSVMVSTB UPQMBNZÐLÐZBS¿BQMBSZMBPSBOUMPMBSBL QBZMBõSMBS :ÐLMÐJMFULFODJTJNMFSJOTJWSJV¿MBSO- EB ZÐL ZPóVOMVóV EJóFS CËMHFMFSF HËSFEBIBGB[MBES qK qL qK' qL' ÖRNEK 1 rK rL rK rL KL :BMULBOBZBLMBSÐ[FSJOFTBCJUMFOFO9 :WF;JMFULFOLÐ- SFMFSJOJOZÐLMFSJTSBTJMF–R –RWF+RZBS¿BQMBSJTF %PLVOEVSVMNBEBOËODF %PLVOEVSVMEVLUBOTPOSB TSBTJMFS SWFSEJS:LÐSFTJ ZBMULBOTBQOEBOUVUV- MBSBLËODF9FTPOSBEB;ZFEPLVOEVSVMVQBZSMZPS qK´ = f qK + qL p.rK qL´ = f qK + qL p.rL XY Z rK + rL rK + rL r 2r 3r CBóOUMBSZMBDJTJNMFSJOZÐLMFSJIFTBQMBOBCJMJS ,ÑSFMFSJOTPOZÑLMFSJOFPMVS :ÐLMÐJLJDJTJNCJSCJSJOFEPLVOEVSVMEVóVOEBUPQlam yük %VSVN %VSVN LPSVOVS %PLVOEVSVMBO DJTJNMFS TPO EVSVNEB ZB BZO DJOTZÐLMFZÐLMFOJSMFSZBEBIFSJLJTJEFOËUSEÐS;UZÐL- - 4q - 2q q' = - 4q + 14q .3r = + 6q MFZÐLMFONFMFSJNÐNLÐOEFóJMEJS q' = .r = - 2q Z 2r + 3r X r + 2r - 4q - 2q q' = - 4q + 14q .2r = + 4q q' = .2r = - 4q Y 2r + 3r Y r + 2r NOT: :ÐLMÐCJSDJTJNOËUSCJSLÐSFOJOJ¿ZÐ[FZJOFTBSL- ÖRNEK 2 UMSTBDJTNJOZÐLÐLFOEJOEFLBMS,ÐSFOJOJ¿JWFEõ[U JõBSFUMFZÐLMFOJS ôFLJMEFLJJMFULFO,WF-LÐSFMFSJOJOZBS¿BQMBSTSBTZMB SWFS ,OJOZÐLNJLUBSJTF-REVS ++ j+ + + m mm m + K L + m m + 3r r ++ + m + + m ++ + + + ++ m + +m + mmm + +q + /ËUS ++ + ++ :ÐLMÐCJSDJTJNJ¿JCPõOËUSCJSLÐSFOJOJ¿ZÐ[FZJne dokun- ,LÑSFTJ-ZFEPLVOEVSVMVQBZSMEôOEB- OJOTPO EVSVMVSTBUÐNZÐLÐOÐLÐSFZFBLUBSSWFDJTJNOËUSPMVS ZÑLÑ+RPMEVôVOBHÌSF -OJOJMLZÑLÑLBÀREVS + + q +q + KL + + q' = .r L r +r L j+ + KL + /ËUS + - 10q + q + ++ L + ++ + 2q = .r + + ++ 3r + r + ++ ++ +q /ËUS + 8q = - 10q + q & q = + 18q +q LL 2 1. qX = –2q, qY = +4q, qZ = +6q 2. +18q

KONUYA HAZIRLIK ##VVTTBBZGZBGEBBELJBJLÀFJSJJÀLFiS&JMLFLiU0SJLMTBFTM,MVLWuWFLUPWOFV&TMFVLZUSMJBL\"JMMHBJOMuJLPOVTTVOZMGBUBJMHHJMÌJSETÑOôÑGUBOÑHÌ[SELÑPôOÑVOMÑB[SLOPOUVFMLBSSBOSUFLBSNBSBBDNZBMDBZIMBBI[BS[MBSMOBONNööUSS Elektriksel Kuvvet ve Elektrik Alan ÷MJöLJMJ,B[BONMBS 9.6.1.3. : &MFLUSJLZÐLMÐDJTJNMFSBSBTOEBLJFULJMFõJNJB¿LMBS &MFLUSJLTFM,VWWFU $PVMPNC,BOVOV ÖRNEK 3 TANIM /Bilgi ôFLJM-EFLJZÐLMFSJOCJSCJSJOFVZHVMBEóFMFLUSJLTFMLVW- \"ZO DJOT ZÐLMF ZÐLMF DJTJNMFSJO CJSCJSJOJ JUUJóJOJ vet F1 ôFLJM-** EFLJ ZÐLMFSJO CJSCJSJOF VZHVMBEó FMFL- [UDJOTZÐLMFZÐLMÐDJTJNMFSJOCJSCJSJOJ¿FLUJóJOJCJ- triksel kuvvet F2 EJS MJZPSV[ +q +2q +q –q /PLUBTBMFMFLUSJLTFMZÐLMFSJOCJSCJSJOFVZHVMBEó JUNFZBEB¿FLNFLVWWFUJOFelektriksel kuvvet d 2d EFOJS ôFLJM* ôFLJM** q1 q2 #VOB HÌSF '1 WF '2 LVWWFUMFSJOJO CÑZÑLMÑLMFSJ LBÀ d F1,2 kqq F2,1 EJS d2 +q +2q k.q.2q F1 F= 12 q1 q2 –q F2 d F1 F2,1 F1,2 d d F =2 kqq 12 d F2 F= k.q.q +q 2 2 F2,1 = F1,2 2d 4d F = k. q1.q2 1 kqq d2 F= . 2 4 2 k = Coulomb sabiti k = 9.109 N.m2 d C2 ÖRNEK 4 \"ZO DJOT ZÐLMFS CJSCJSJOJ FõJU CÐZÐLMÐLUFLJ LVW- /PLUBTBMR1WFR2 ZÐLMFSJZBMULBO[FNJOEFBSBMBSOEBE WFUMF JUFSLFO GBSLM DJOT ZÐLMFS FõJU CÐZÐLMÐLUFLJ V[BLMóCVMVOBDBLõFLJMEFLPOVMEVóVOEBR1JOR2 yi it- LVWWFUMF¿FLFS me kuvveti F2 R2OJOR1 i itme kuvveti F1 PMVZPS :ÐLMÐ JLJ DJTNJO CJSCJSJOF VZHVMBEó FMFLUSJLTFM q1 q2 LVWWFUJO CÐZÐLMÐóÐ DJTJNMFSJO ZÐLMFSJOJO CÐZÐL- F2 F1 MÐóÐOÐO¿BSQNJMFEPóSV BSBMBSOEBLJV[BLMóO LBSFTJJMFUFSTPSBOUMES d ,VWWFU WFLUËSFM PMBSBL ZËOÐ EJLLBUF BMOBSBL HËTUFSJMEJóJJ¿JOGPSNÐMEFZÐLJõBSFUJEJLLBUFBMO- #VOBHÌSF NBEBOIFTBQMBNBZBQMS * R1R2 ise F1 = F2 ** R2R1 ise F2 > F1 *** R1R2 ise F1 = F2 EVSVNMBSOEBOIBOHJMFSJEPôSVEVS :ÑLMÑ DJTJNMFSJO ZÑL CÑZÑLMÑLMFSJ BSBTOEBLJ JMJöLJ OF PMVSTB PMTVO CJSCJSMFSJOJ FöJU CÑZÑLMÑLUFLJ FMFLUSJLTFM LVWWFUMFJUFSWFZBÀFLFSMFS$FWBQ*WF*** 3 3. 2, 1 4. I ve III 4

KONUYA HAZIRLIK #VTBZGBEBLJJÀFSJLi&MFLUSJLTFM,VWWFUWF&MFLUSJL\"MBOuLPOVTVZMBJMHJMJTOGUBHÌSEÑôÑOÑ[LPOVMBSOUFLSBSBNBDZMBIB[SMBONöUS Elektriksel Kuvvet ve Elektrik Alan ÷MJöLJMJ,B[BONMBS 9.6.1.4. : &MFLUSJLBMBOLBWSBNOB¿LMBS Elektrik Alan 4BCJU ZÐLMFSJO PMVõUVSEVóV FMFLUSJL BMBO ¿J[HJMFSJ ( + ZÐLUFO - ZÐLFEPóSVZËOFMJS TANIM /Bilgi +– &MFLUSJLTFM ZÐLÐO FULJTJOJ HËTUFSEJóJ CËMHFZF P yükün FMFLUSJLTFMBMBOEFOJS + #JS OPLUBEBLJ FMFLUSJL BMBO õJEEFUJ P OPLUBEBLJ +CJSJNMJLZÐLF CZ FULJFEFOFMFLUSJLTFMLVW- WFULBEBSES +q +1 by F –q +1 by d F d k.q + E = d2 CBóOUTJMFIFTBQMBOS k : Coulomb sabiti 7FLUËSFM ZËOMÐ CJSCÐZÐLMÐLUÐS ÖRNEK 5 –– * :ÐLMÐQBS¿BDLMBSO¿FWSFTJOEFLJFMFLUSJLBMBOCÐ- ÖRNEK 6 ZÐLMÐóÐQBS¿BDóBZBLMBõUL¿BBSUBS &MFLUSJLMFZÐLMÐ9WF:LÐSFMFSJOJOFMFLUSJLBMBO¿J[HJMFSJ ** :ÐLMÐ QBS¿BDLMBSO ¿FWSFTJOEF PMVõBO FMFLUSJL õFLJMEFWFSJMNJõUJS BMBOõJEEFUJPSUBNODJOTJOFCBóMES XY *** :ÐLMÐ QBS¿BDLMBSO PMVõUVSEVóV FMFLUSJL BMBO QBS- ¿BDóOZÐLNJLUBSBSUUL¿BBSUBS #VOBHÌSF 9WF:LÑSFMFSJOJOZÑLNJLUBSMBSWFZÑL DJOTMFSJOBTMES ZBSHMBSOEBOIBOHJMFSJEPôSVEVS &MFLUSJL BMBO ÀJ[HJMFSJ + ZÑLUFO - ZÑLF EPôSV ZÌOF- :ÑLMÑ QBSÀBDLMBS ÀFWSFMFSJOEF FMFLUSJL BMBO FULJTJ ZBSB- MJS#VEVSVNEB9 - ZÑLMÑ : + ZÑLMÑEÑS&MFLUSJLBMBO USMBS #V BMBO QBSÀBDôB ZBLMBöULÀB BSUBS V[BLMBöULÀB ÀJ[HJMFSJOJOTLPMEVôVCÌMHFEFFMFLUSJLBMBOöJEEFUJCÑ- B[BMS ZÑLTFZSFLPMEVôVCÌMHFEFLÑÀÑLPMVS#VZÑ[EFO9DJT- :ÑLMÑ QBSÀBDôO ZÑLÑ OF LBEBS CÑZÑLTF PMVöUVSEVôV NJOJOZÑLNJLUBS:EFOLÑÀÑLUÑS$FWBQ RX < qY FMFLUSJLBMBOFULJTJEFPLBEBSCÑZÑLPMVS&MFLUSJLBMBO WFLUÌSFMCJSCÑZÑLMÑLUÑS$FWBQ* **WF*** Bilgi &MFLUSJLBMBOLVWWFU¿J[HJMFSJ + ZÐLUFOEõBEPó- SVEVS - ZÐLUFJTFEõUBOZÐLFEPóSVEVS EE +– 5. I, II ve III 4 6. 9 m : qX < qY

TEST - 1 #VTBZGBEBLJJÀFSJLi&MFLUSJLTFM,VWWFUWF&MFLUSJL\"MBOuLPOVTVZMBJMHJMJTOGUBHÌSEÑôÑOÑ[LPOVMBSOUFLSBSBNBDZMBIB[SMBONöUS 1. R1 WF R2 ZÐLMÐ JLJ DJTJN CJSCJSJOJ FõJU CÐZÐLMÐLUFLJ 4. ôFLJMEFLJZÐLMÐDJTJNMFSEFO,WF.TBCJUUVUVMVSLFO LVWWFUMF¿ekiyorlaS -TFSCFTUCSBLMZPS #VEVSVNMBJMHJMJ 10 cm 10 cm * R1R2 qK = 2.10–5C qL = 10–6C qM = 10–5C ** $JTJNMFS[UJõBSFUMFZÐLMÐEÐS #VOB HÌSF - DJTNJOF FULJ FEFO OFU LVWWFUJO *** $JTJNMFSJO õFLMJ LVWWFUJO CÐZÐLMÐóÐOÐ FULJMF- ZÌOÑWFCÑZÑLMÑôÑLBÀOFXUPOEVS NF[ f k = 9.109 Nm2 p ZBSHMBSOEBOIBOHJMFSJkesinlikleEPôSVEVS C2 \" :BMO[* # :BMO[** $ :BMO[*** A) 9 N B) 9 N C) 18 N % *WF** & **WF*** D) 18 N E) 20 N 2. öLJZÐL BSBMBSOEBLJV[BLMLEJLFOCJSCJSMFSJOF 5. &MFLUSJLTFMBMBOJMFJMHJMJBöBôEBWFSJMFOCJMHJMFS- /MVLLVWWFUVZHVMVZPSMBS EFOIBOHJTJEPôSVEVS #V ZÑLMFSEFO CJSJOJO ZÑLÑ LBUOB ÀLBSMQ \" 4LBMFSCJSCÐZÐLMÐLUÐS BSBMBSOEBLJ V[BLML ZBSZB JOEJSJMJSTF BSBMBSO- EBLJLVWWFULBÀOFXUPOPMVS # :ÐLMÐQBS¿BDóOZÐLNJLUBSOBCBóMEFóJMEJS \" # $ % & $ :ÐLMÐQBS¿BDLUBOV[BLMBõUL¿BBSUBS % #JSOPLUBEBFMFLUSJLBMBOPMVõNBTJ¿JO+1 birim- MJLZÐLFJIUJZB¿WBSES & &MFLUSJLBMBO¿J[HJMFSJ + ZÐLUFO - ZÐLFEPóSV ZËOFMJS 3. ±[EFõJMFULFO9WF:LÐSFMFSJõFLJMEFLJHJCJZÐLMF- 6. :ÐLMÐJLJDJTJNBSBTOEBLJFMFLUSJLTFMLVWWFU ' DJ- OJQBSBMBSOEBLJV[BLMLEPMBDBLõFLJMEFLPOVMEV- TJNMFSBSBTOEBLJV[BLMóO E LBSFTJJMFUFSTPSBO- óVOEB9JO:ZFVZHVMBEóFMFLUSJLTFMLVWWFUJOCÐ- UMES ZÐLMÐóÐ/PMVZPS #VOBHÌSF BöBôEBLJMFSEFOIBOHJTJEPôSVEVS qX = +8q qY = –2q A) F B) F C) F r r XY 0 d2 0 d2 0 d2 d ,ÑSFMFS CJSCJSJOF EPLVOEVSVMVQ BZO V[BLMôB D) F E) F LPOVMEVôVOEBCVLVWWFULBÀOFXUPOPMVS 0 d2 0 d2 \" # $ % & 1. E 2. A 3. C 5 4. B 5. E 6. E

11. SINIF .0%·- &-&,53÷,4&-,677&5\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinya·y/in÷5la&ri.com.tr Elektriksel Kuvvet ve Elektrik Alan ÷MJöLJMJ,B[BONMBS 11.2.1.1. : :ÐLMÐDJTJNMFSBSBTOEBLJFMFLUSJLTFMLVWWFUJFULJMFZFOEFóJõLFOMFSJCFMJSMFS Elektriksel Kuvvet ÖRNEK 7 7ANnM%m/*m \"SBMBSOEBEV[BLMLCVMVOBO-RZÐLMÐ,LÐSFTJWF+R ZÐLMÐ - LÐSFTJOJO CJSCJSMFSJOF VZHVMBELMBS FMFLUSJLTFM &MFLUSJL ZÐLÐ JMF ZÐLMFONJõ OPLUBTBM DJTJNMFSJO LVWWFUJOCÐZÐLMÐóÐ'LBEBSES CJSCJSMFSJOF VZHVMBEó JUNF WFZB ¿FLNF LVWWF- tine elektriksel kuvvetEFOJS –q +4q r 2r Bu kuvvete $PVMPNCLVWWFUJEFEFOJS K L öMLLF['SBOT[CJMJNJOTBO$IBSMFT$PVMPNCUB- 3d SBGOEBOJODFMFONJõUJS :BSÀBQMBS WFSJMFO LÑSFMFS CJSCJSJOF EPLVOEVSVMVQ $PVMPNC JLJ FMFLUSJL ZÐLÐ BSBTOEBLJ LVWWFUJO BSBMBSOEBLJ V[BLML E ZBQMSTB VZHVMBELMBS FMFL- õJEEFUJOJOZÐLMFSJO¿BSQNJMFEPóSV BSBMBSOEB- USJLTFMLVWWFUJOCÑZÑLMÑôÑLBÀ'PMVS LJV[BLMóOLBSFTJJMFUFSTPSBOUMPMEVóVOVHËS- EÐ q.4q 2 F = k. q9 & k. = F q1 q2 2 2 4 d F1,2 9d d F2,1 q' = - q + 4q .r K r + 2r q1 q2 q ' = - q + 4q .2r F2,1 F1,2 L r + 2r d q.2q 1 kq 2 Fl = k. . & Fl = 2 2 2 d 4d F2,1 = F1,2 Fl = 1 9 F . 24 F = k. q1.q2 $FWBQFl = 9 F d2 8 ÖRNEK 8 k = Coulomb sabiti :ÑLMÑ QBSÀBDLMBS BSBTOEBLJ FMFLUSJLTFM LVWWFUMF JM- k = 9.109 N.m2 HJMJ C2 * 1BS¿BDLMBSOZÐLMFSJOJO¿BSQNJMFEPóSVPSBOUMES ** \"SBMBSOEBLJV[BLMóOLBSFTJJMFUFSTPSBOUMES \"ZOJõBSFUMJZÐLMFSCJSCJSJOJJUFS [UJõBSFUMJZÐLMFS *** BirbirineFõJUWF[UZËOMÐEÐS CJSCJSJOJ¿FLFS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS 6IMpLASYONUVAR ÷LJ FMFLUSJL ZÑLÑ BSBTOEBLJ LVWWFU ZÑLMFSJO ÀBSQN JMF EPôSV BSBMBSOEBLJV[BLMôOLBSFTJJMFUFSTPSBOUMES #VLPOVJMFJMHJMJEFOFZWJEFP- MBS WFZB TJNÐMBTZPOMBSB ZBO- q .q daki 2SLPEJMFVMBõBCJMJSTJOJ[ f F = k. 1 2 p 2 d F F F F + + + – $FWBQ* ** *** 6 9 7. F 8. I, II ve III 8

www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" .0%·- 11. SINIF .qk(7$k, ÖRNEK 10 $PVMPNCZBTBTOEBLJMFHËTUFSJMFOPSBOUTBCJ- \"ZOEPóSVMUVÐ[FSJOEFCVMVOBOR1 R2WFR yüklerinden tine $PVMPNCTBCJUJEFOJS R2TFSCFTUCSBLMEóOEBEFOHFEFLBMZPS #V TBCJU ZÐLMFSJO J¿JOEF CVMVOEVóV PSUBNO DJOTJOFCBóMPMBSBLEFóJõJS q1 q2 q3 )BWBWFCPõMVLJ¿JOk , 9.109 N.m2 EJS 2d d C2 q k = 1 & f = 1 = 8, 85.10–12 C2 #VOBHÌSF 1 PSBOLBÀUS 4πf 0 4πk N.m2 q 0 3 f0 =#PõMVóVOFMFLUSJLHF¿JSHFOMJóJ q2OJOEFOHFEFLBMNBöBSUR1 ve q3ZÑLMFSJOJOFöJUCÑZÑLMÑLUF WF[UZÌOMÑLVWWFUVZHVMBNBTJMFPMVS k.q .q k.q .q 12 23 F1,2 = F3,2 = ÖRNEK 9 22 4d d \"SBMBSOEBELBEBSV[BLMLCVMVOBO + ZÐLMÐ,WF-DJ- q TJNMFSJCJSCJSMFSJOF'CÐZÐLMÐóÐOEFFMFLUSJLTFMLVWWFUuy- HVMBNBLUBES 1 =4 q 3 $FWBQ + d ÖRNEK 11 FK + LF &õJUCËMNFMFOEJSJMNJõEÐ[MFNFZFSMFõUJSJMFOR1WFR2 yükle- rinin -RZÐLÐOFVZHVMBELMBSLVWWFUMFSJOCJMFõLFTJ F EJS #VOBHÌSF * ,DJTNJOJOZÐLNJLUBSOBSUUSNBL ** EV[BLMóOB[BMUNBL *** 0SUBNOFMFLUSJLHF¿JSHFOMJóJOJB[BMUNBL IBOHJMFSJOJOZBQMNBT'JBSUUSS F &MFLUSJLTFM LVWWFU ZÑLMFSJO ÀBSQN JMF EPôSV ZÑLMFS BSBT 1 br q1 V[BLMôOLBSFTJJMFUFSTPSBOUMES 3 br –q 11 2 br 1 br k= & k.a f PMEVôVOEBOfB[BMSTBLBSUBS 4πf q2 0 0 q .q q #VOBHÌSF 1 PSBOLBÀUS 12 q F = k. 2 PMEVôVJÀJO'BSUBS d 2 $FWBQ* ** *** ¦PL4BZEB:ÑLÑO$PVMPNC,VWWFUJ ¦J[JNEFO ÀLBSBDBôN[ TPOVÀ R1 in -R ZÑLÑOÑ CJSJNMJL LVWWFUMFJUUJôJ R2 nin -RZÑLÑOÑCJSJNMJLLVWWFUMFJUUJôJEJS %m/*m #VOVOTPOVDVOEBR1 ve q2ZÑLMFSJOJO - JöBSFUMJPMEVôVOB EJLLBUFEJMNFMJEJS &óFSPSUBNEBJLJEFOGB[MBZÐLWBSTBCVOMBSEBOIFS- IBOHJCJSJÐ[FSJOEFLJOFULVWWFUEJóFSZÐLMFSJOCVOB q .q VZHVMBELMBSLVWWFUMFSJOWFLUÌSFMUPQMBN PMVS 1 +q2 3 = k. & kq .q = 12 F4,1 41 F3,1 q .q –q3 +q1 2 1 = k. & kq .q = 1 12 q 1 = 12 q 2 +q4 F2,1 $FWBQ 9. I, II, III 7 4 11. 12

11. SINIF .0%·- &-&,53÷,4&-,677&5\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr %m/*m ÖRNEK 13 T1 ab T2 %ÐõFZEÐ[MFNEFCVMVOBOZÐLMFSJR1 R2 kütleleri m1, m2 öQ öQ PMBO WF UBWBOB ZBMULBO JQMFSF BTMNõ JLJ LÐSF õFLJMEFLJ F2,1 q1 HJCJEFOHFEFEJS a m1 q2 F1,2 m2 b öQ ab öQ T1 T2 m1g m2g F2,1 q1 \"ZODJOTFMFLUSJLZÐLÐOFTBIJQJLJDJTJNõFLJMEFLJ q2 F1,2 HJCJEÐõFZEÐ[MFNEFPMBDBLCJ¿JNEFBTMSTBZÐL CÐZÐLMÐLMFSJOFPMVSTBPMTVOCJSCJSMFSJOJBZOCÐ- m1g m2g yüklükteki elektriksel kuvvetlerle iterler ve yuka- SEBLJHJCJEFOHFEFLBMSMBS a < bPMEVôVOBHÌSF QBSÀBDLMBSOLÑUMFMFSJ ZÑLCÑ- ZÑLMÑLMFSJ BSBMBSOEBLJFMFLUSJLTFMLVWWFUWFJQMFSEF- öQMFSJOEÐõFZMFZBQULMBSB¿MBSDJTJNMFSJOBóSML- LJHFSJMNFLVWWFUMFSJBSBTOEBLJJMJöLJMFSOBTMES MBSOBCBóMPMBSBLEFóJõJLMJLHËTUFSJS F1,2 = F2,1 ise; F1,2 = F2,1 dir. F2, 1 F1, 2 tan a = m m > m dir. tan a = tan b = 2 12 m1g m2g tan b m 1 :ÑLCÑZÑLMÑLMFSJJMFJMHJMJLFTJOCJSöFZTÌZMFOFNF[ tan a = F2,1 . m2g & tan a = m2 olur. ÷QMFSEFLJHFSJMNFLVWWFUMFSJFMFLUSJLTFMLVWWFUMFBôSMôOCJ- tan b m1g F1,2 tan b m1 MFöLFTJPMEVôVOEBO51 > T2EJS$FWBQN1 >N2 '1 ='2 ZÑLMFSMFJMHJMJCJSöFZTÌZMFOFNF[ m1 = m2 ise a = bES m1 > m2 ise a < bES ÖRNEK 14 m1 < m2 ise a > bES %ÐõFZ EÐ[MFNEF ZÐLMFSJ R1 WF R2, kütleleri m1 ve m2 öQMFSEFLJHFSJMNFLVWWFUMFSJOJOCÐZÐLMÐLMFSJDJTNF PMBO WF UBWBOB ZBMULBO JQMFSF BTMNõ LÐSFMFS õFLJMEFLJ HJCJEFOHFEFEJS FULJ FEFO FMFLUSJLTFM LVWWFUJO CÐZÐLMÐóÐ JMF DJT- A 2k O k B NJOBóSMóOOCJMFõLFTJOJOCÐZÐLMÐóÐOFFõJUUJS ÖRNEK 12 aa öQ öQ ø %ÐõFZ EÐ[MFNEF ZBMULBO JQMFSF BTMNõ BSBMBSOEB- 2ø LJ NFTBGF E PMBO Ë[EFõ WF +R ZÐLMÐ JLJ LÐSFTFM DJTNJO LÐUMFMFSJNLBEBSWFCJSCJSMFSJOFVZHVMBELMBSFMFLUSJLTFM LVWWFUJOõJEEFUJ'EJS a öQ m2g öQ m1g +q +q m d #VOBHÌSF DJTJNMFSJOLÑUMFMFSJPSBO 1 LBÀUS #VOBHÌSFNEFôFSJBSUUSMSTBaWF'OBTMEFôJöJS m 2 $JTJNMFSJOLÑUMFMFSJJMFJQMFSJOEÑöFZMFZBQUôBÀUFSTPSBO- 5BSBMÑÀHFOMFSJOCFO[FSMJôJOEFO| AO | = 2.| OB | dir. UMES#VZÑ[EFOaBÀTB[BMSaBÀTOOB[BMNBTDJTJNMFS BSBTOEBLJEV[BLMôOOB[BMNBTOBTFCFQPMVS#VEVSVN- \"ôSMLMBSO0OPLUBTOBHÌSFUPSLMBSFöJUPMNBMES EBDJTJNMFSCJSCJSMFSJOJEBIBCÑZÑLCJSLVWWFUMFJUFS$FWBQ aB[BMS 'BSUBS m = 1 PMVS$FWBQ 1 1 m 2 2 2 12. aB[BMS 'BSUBS 8 1 13.N1N2 '1'2ZÑLMFSMFJMHJMJCJSöFZTÌZMFOFNF[14. 2

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www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" .0%·- 11. SINIF Elektriksel Kuvvet ve Elektrik Alan ÷MJöLJMJ,B[BONMBS 11.2.1.2. : /PLUBTBMZÐLJ¿JOFMFLUSJLBMBOB¿LMBS Elektriksel Alan ÖRNEK 18 ôFLJM-1 deki -R ZÐLÐOÐO 9 OPLUBTOEB PMVõUVSEVóV 7ANnM%m/*m elektrik alan EX ôFLJM-2 deki +RZÐLÐOÐO:OPLUBTO- EBPMVõUVSEVóVFMFLUSJLBMBO EY EJS &MFLUSJLTFMCJSZÐLÐOFULJTJOJOPMEVóVCËMHFZFP yükün FMFLUSJLTFMBMBOEFOJS –q +q X Y &MFLUSJLTFMBMBOJ¿JOEFCVMVOBOIFSIBOHJCJSOPL- d d UBEBLJ FMFLUSJL BMBO õJEEFUJ P OPLUBZB LPOVMBO ôFLJMm* 2 R= +CJSJNMJL UFTUZÐLÐ ZÐLFFULJFEFOFMFL- ôFLJMm** USJLTFMLVWWFUPMBSBLUBONMBOS #VOBHÌSF EX / EY PSBOLBÀUS &MFLUSJLBMBOWFLUËSFMCJSCÐZÐLMÐLUÐS E JMFHËT- UFSJMJS 4FÀJMFOOPLUBMBSB+CZLPZBSTBL +Q q = +1 by –Q –q E'X +1 by +q +1 by EY F q = +1 by d d 2 F d d –q q 4q d2 d2 E'X = k. E'Y = k. d 2 =k 2 E= F, k.q.Q E = k.Q ( ) F= q d2 & d2 E'X = –1 E'Y 4 1 $FWBQ - 4 Elektrik alan birimi Newton EVS ÖRNEK 19 Coulomb Elektriksel alanla ilgili, &MFLUSJLTFMBMBO UFTUZÐLÐPMBOREBOCBóNT[ES * :ÐLMÐ QBS¿BDLMBSO ¿FWSFTJOEF PMVõUVSEVóV FMFL- USJLBMBOõJEEFUJQBS¿BDóOZÐLNJLUBSOBCBóMES &MFLUSJLTFMBMBO2ZÐLÐJMFEPóSV ZÐLÐOTF¿JMFO ** :ÐLMÐQBS¿BDLUBOV[BLMBõUL¿BFMFLUSJLBMBOõJEEF- OPLUBZB PMBO V[BLMóOO LBSFTJ JMF UFST PSBOUM UJB[BMS PMVQBZO[BNBOEBPSUBNODJOTJOFEFCBóMES *** &MFLUSJLTFMBMBOWFLUËSFMCJSCÐZÐLMÐLUÐS ÖRNEK 17 WFSJMFOJGBEFMFSEFOIBOHJMFSJEPôSVEVS +RZÐLMÐCJSDJTNJOLFOEJTJOEFOELBEBSV[BLUBPMVõUVS- 1BSÀBDLMBSO ZÑL NJLUBS ÀFWSFTJOEFLJ FMFLUSJL BMBO öJEEF- EVóVFMFLUSJLTFMBMBOõJEEFUJ&EJS UJOJBSUUSS1BSÀBDLMBSOFMFLUSJLBMBOöJEEFUJV[BLMLMBUFST PSBOUMES&MFLUSJLTFMBMBOZÌOMÑCJSCÑZÑLMÑLUÑS #VOBHÌSF BZOPSUBNEB-RZÑLMÑCJSDJTNJOLFOEJ- sinden d LBEBSV[BLUBPMVöUVSEVôVFMFLUSJLTFMBMBO $FWBQ* ** *** 2 &MFLUSJL\"MBO,VWWFU¦J[HJMFSJ öJEEFUJLBÀ&PMVS 7ANnM%m/*m &MFLUSJLTFM BMBO LVWWFU ¿J[HJMFSJOJO ZËOÐ QP[JUJG 4FÀJMFOOPLUBMBSB+CZLPZBSTBL ZÐLUFO EõBS EPóSV OFHBUJG ZÐLUF JTF EõBSEBO ZÐLFEPóSVEVS +2q +1 E –q E' +1 EE d d E = k 2q 2 +– d2 E' = k kq = 4kq ( d ) 2 d2 2 Cevap: E' = 2E 17. 2E 11 - 1 18. 19. I, II ve III 4

11. SINIF .0%·- &-&,53÷,4&-,677&5\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr &MFLUSJL\"MBO,VWWFU¦J[HJMFSJ 7ANnM%m/*m %m/*m &MFLUSJLBMBOLVWWFU¿J[HJMFSJCJSCJSMFSJOJLFTNF[MFS 1P[JUJGCJS2ZÐLÐZÐL- TÐ[ JMFULFO LÐSFTFM CJS + +– – .FUBM LBCVL õFLMJOEFLJ NF- JMFULFO UBM JMFULFO JMF ¿FWSJMEJ- :ÐLUFCBõMBZBOWFZBTPOMBOBOBMBOLVWWFU¿J[HJ- + Q óJOEF NFUBMJ¿JOEFCJS MFSJOJOTBZTZÐLNJLUBSJMFEPóSVPSBOUMES elektrik alan olamaya- DBó J¿JO 2 ZÐLÐOEFO – –Q +2Q + ¿LBO ¿J[HJMFS NFUBMJO J¿ ZÐ[FZJOEFLJ OFHBUJG &MFLUSJL BMBO LVWWFU ¿J[HJMFSJ FMFLUSJLTFM BMBOO yükler üstünde sona õJEEFUMJ PMEVóV ZFSEF TL BMBOO [BZG PMEVóV FSFDFLUJS#BõMBOH¿UBZÐLTÐ[PMBOLÐSFTFMLBCV- ZFSEFTFZSFLUJSMFS óVOJ¿ZÐ[FZJOEFCJSJLFO - ZÐLLBEBSEõZÐ[F- yinde de (+ ZÐL CJSJLUJóJOF EJLLBU FEJMNFMJEJS Sabit tutulan (+ WF - ZÐLMFSJOJO PMVõUVSEVóV .FUBMJO J¿JOEF BMBO CVMVONBNBTOB SBóNFO E- FMFLUSJL BMBO LVWWFU ¿J[HJMFSJ + ZÐLMÐ DJTJNEFO õOEBTBOLJNFUBMZPLNVõHJCJFMFLUSJLBMBOWBS- ¿LBSBL - ZÐLMÐDJTNFHJSFDFLõFLJMEFPMVS ES 'BSBEBZ,BGFTJ E E + – E –– &MFLUSJLBMBOLVWFU¿J[HJMFSJFMFLUSJLBMBOOZËOÐ- OÐHËTUFSJS&MFLUSJLBMBOIFSOPLUBEBBMBO¿J[HJ- –– MFSJOFUFóFUUJS –– E %Ð[HÐO FMFLUSJLTFM BMBO FõJU BSBMLM QBSBMFM EPóSV- –– MBSõFLMJOEFEJS :ÐLTÐ[J¿JCPõNFUBMCJSLVUVJLJQBSBMFMZÐLMÐMFW- 7ANnM%m/*m :ÐLMÐ JMFULFO LÐSFOJO IBBSBTOBCSBLMEóOEBLVUVÐ[FSJOEFõFLJMEF- J¿JOEF FMFLUSJL BMBO PMVõ- LJHJCJFMFLUSJLBMBO¿J[HJMFSJPMVõVS#VZPMMBLVM- E=0 NB[ ,ÐSF ZÐ[FZJOEF WF MBOMBOJMFULFONFUBMLVUVIBTTBTBMFUMFSWFFMFL- EõOEB PMVõBO FMFLUSJL USPOJLEFWSFMFSJOJJTUFONFZFOEõFMFLUSJLBMBOMBS- –r O +r BMBOIFTBQMBOSLFOLÐSF- EBOLPSVNBLJ¿JOFULJMJCJSTJTUFNEJS TFMTJNFUSJEFOEPMBZUÐN ZÐLÐO LÐSF ZÐ[FZJOEF ÖRNEK 20 UPQMBOEóEÐõÐOÐMÐS ö¿J¿FHF¿NJõJMFULFOWFZÐLMÐJ¿JCPõLÐSFMFSJOZÐLMFSJ+Q ve -2EVS +Q –2Q * ** *** #VOB HÌSF * ** WF *** CÌMHFMFSEFLJ FMFLUSJLTFM BMBO ÀJ[HJMFSJOBTMPMVS 12

&-&,53÷,4&-,677&57&&-&,53÷,\"-\"/ TEST - 3 1. ôFLJMEFLJ HJCJ J¿ J¿F LPONVõ Fõ NFSLF[MJ LÐSFMFS 4. ôFLJMEF OËUSCJSNFUBMMFWIBEÐ[HÐO E elektrik ala- +RZÐLMÐEÐS OOBQBSBMFMCJSõFLJMEFLPONVõUVS E OP R r rr rr 2r +q +q E 1 OPLUBTOEBLJ FMFLUSJLT FM BMBO & JTF 3 EFLJ #VOBHÌSF MFWIBEBLJZÑLEBôMNOBTMPMVS FMFLUSJLTFMBMBOLBÀ&EJS \" 1 # 2 $ % 4 & 3 A) + + + + B) – – – – C) – + 2 3 32 + ––– – ++++ – + – + – 2. \"ZOEÐ[MFNEFLJ+R –RWF–ROPLUBTBMZÐL- D) + – E) MFSJOJO0NFSLF[MJEBJSFÐ[FSJOFõFLJMEFLJHJCJLPO- +– +– +– NVõUVS+RZÐLÐOÐO0OPLUBTOEBLJFMFLUSJLTel BMBO E EJS +q –2q –2q 6600°° O #VOBHÌSF 0OPLUBTOEBLJCJMFöLFFMFLUSJLTFM 5. ö¿JCPõCÐZÐLLÐSFOJOZÐLÐ+2EVS#VOVOJ¿FSJTJ- BMBOOFPMVS (sin 60° = 3 ; cos 60° = 1 ) 22 ne –2ZÐLMÐJ¿JCPõLÐ¿ÐLCJSLÐSFZFSMFõUJSJMNJõUJS +Q \" E # - E $ 2E % -2E & 3E –Q 3. ,POVNMBSõFLJMEFLJHJCJPMBOBZOEÐ[MFNEFLJOPL- UBTBM R1 = –R WF R2 ZÐLMFSJOJO - OPLUBTOEB PMVõUVSEVóVCJMFõLFFMFLUSJLT Fl alan E EJS q1 = –8q L #VTJTUFNEFFMFLUSJLTFMBMBOÀJ[HJMFSJOBTMPMVS q2 A) B) C) E D) E) #VOB HÌSF R2 ZÑLÑ BöBôEBL JMFSEFO IBOHJTJ EJS #ÌMNFMFSFõJUBSBMLM \" mR # mR $ mR % mR & +R 1. A 2. B 3. B 13 4. D 5. E

11. SINIF .0%·- &-&,53÷,4&-,677&5\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr Elektriksel Kuvvet ve Elektrik Alan ÷MJöLJMJ,B[BONMBS 11.2.1.3. : /PLUBTBMZÐLMFSEFFMFLUSJLTFMLVWWFUWFFMFLUSJLBMBOJMFJMHJMJIFTBQMBNBMBSZBQBS %m/*m ÖRNEK 22 E E2 \"ZOEÐ[MFNEFCVMVOBOOPLUBTBMR1 = +R R2 = -R R = -RZÐLMFSJOJOLPOVNMBSõFLJMEFLJHJCJEJS d1 +q1 E1 +1 q1 = q d2 d d q2 = –2q O d +q2 #JSEFOGB[MBZÐLÐOCJSOPLUBEBPMVõUVSEVóVFMFL- q3 = –q USJL BMBO CVMVOVSLFO IFS CJS ZÐLÐO P OPLUBEB PMVõUVSEVóV FMFLUSJL BMBO CVMVOVQ WFLUËSFM PMB- #VOB HÌSF ZÑLMFSJO 0 OPLUBTOEB PMVöUVSEVLMBS SBLUPQMBOS q elektrik alan öJEEFUJLBÀk EJS d2 +q –2q k.2q k.2q d2 E3 = d2 kq kq k.2q kq E1 = d2 E2 = d2 d2 ECJMFöLF = 2 2 d2 –q $FWBQ 2 2 ÖRNEK 21 ôFLJMEFBSBMBSOEBELBEBSV[BLMLCVMVOBOTBCJUR1 ve ÖRNEK 23 R2 yükMFSJWFSJMNJõUJS \"ZOEÐ[MFNEFCVMVOBOõFLJMEFFMFLUSJLZÐLMÐ9 :WF; 1.bölge 2.bölge 3.bölge LÐSFMFSJOJOLPOVNVJMFFMFLUSJLBMBOLVWWFU¿J[HJMFSJOJOCJ- ¿JNJWFZËOÐWFSJMNJõUJS E1 q1= +4q E1 q2= +16q E1 E2 d x E2 d–x X Y M Z KL E2 #VOB HÌSF FMFLUSJL BMBO öJEEFUJ R2 ZÑLÑOEFO LBÀ E V[BLUBTGSPMVS :ÑLMÑ DJTJNMFSJO * WF *** CÌMHFEF PMVöUVSEVôV FMFLUSJLTFM , WF . OPLUBMBSOEB FMFLUSJL BMBO öJEEFUJ TGSES 9 LÑSFTJOJO ZÑL NJLUBS R JTF : WF ; LÑSFMFSJOJO ZÑL BMBOMBS BZO ZÌOMÑ PMEVôVOEBO CV CÌMHFMFSEF FMFLUSJLTFM NJLUBSLBÀRPMVS /PLUBMBSBSBTFõJUBSBMLMES BMBOTGSPMBNB[**CÌMHFEFDJTJNMFSJOPMVöUVSEVôVFMFLUSJL- TFMBMBOMBS[UZÌOMÑPMEVôVOEBOCVCÌMHFEFFMFLUSJLBMBOO TGSPMBDBôCJSOPLUBWBSES#VOPLUBOOR2ZÑLÑOFV[BLM- ,OPLUBTOEBLJFMFLUSJLBMBOöJEEFUJOJOTGSPMNBT9WF:LÑSF- ôOBYEFSTFLCVOPLUBEBFMFLUSJLTFMBMBOöJEEFUMFSJFöJUPMB- MFSJOJOPOPLUBEBLJFMFLUSJLBMBOMBSOOFöJUMJôJJMFNÑNLÑOEÑS DBôOEBO E =E .OPLUBTOEBLJFMFL- USJL BMBO öJEEFUJOJO XY TGS PMNBT : WF ; LÑSFMFSJOJO P OPLUB- E =E 4q q k. = k. q = 16q 12 Y Y 4q 16q 1 2 22 k. = d 4d k. & d - x = x & 2d - 2x = x ^ d - x h2 2d = 3x EBLJFMFLUSJLBMBOMBSOOFöJUMJôJJMFNÑNLÑOEÑS 2 x 2d 16q q q = 16q ,VWWFU ÀJ[HJMFSJOJO ZÌ- x= k. = k. OÑEöBSEBOZÑLFEPô- Z Z SV PMEVôVOB HÌSF ZÑL- 3 22 dd 2d $FWBQ ler (- JöBSFUMJEJS$FWBQRY = -16q, qZ = -16q 3 2d 14 22. 2 2 23. qY = -16q, qZ = -16q 21. 3

&-&,53÷,4&-,677&57&&-&,53÷,\"-\"/ TEST - 4 1. #JS OFTOFOJO FMFLUSJL ZÐLÐOEFO LPSVONBTOB ZBS- 4. \"ZOEÐ[MFNEFCVMVOBOFMFLUSJLZÐLMÐ9WF:LÐSF- ENDPMBOEÐ[FOFLMFSFGBSBEBZLBGFTJBEWFSJMJS MFSJOJO¿FWSFTJOEFLJFMFLUSJLBMBOLVWWFU¿J[HJMFSJõF- LJMEFLJHJCJEJS * :BODWFQBUMBZDNBEEFMFSJOEFQPMBOEóCJ- OBMBS ** 5FMTJ[IBCFSMFõNFTJOJOZBQMEóCJOBMBS *** .3DJIB[MBSOOZFSMFõUJSJMEJóJPSUBNMBS XY WFSJMFOÌSOFLMFSEFOIBOHJMFSJ'BSBEBZ,BGFTJJMF JMHJMJEJS \" :BMO[* # :BMO[*** $ *WF** % *WF*** & * **WF*** #VOBHÌSF * 9 ZÐLMÐ : - ZÐLMÐEÐS 2. 4ÐSUÐONFTJ[ ZBUBZ EÐ[MFNEF CVMVOBO OPLUBTBM ** 9JOZÐLNJLUBS :OJOZÐLNJLUBSOEBOGB[MBES +RWF-RZÐLMFSJõFLJMEFLJHJCJTBCJUUVUVMNBLUBES *** 9WF:[UJõBSFUMJEJS 2 1 +2q JGBEFMFSJOEFOIBOHJMFSJEPôSVEVS 3 \" :BMO[* # :BMO[** $ *WF** –q % *WF*** & * **WF*** O 4 –q 5. ôFLJMEFLJHJCJZBMULBOEÐ[MFNEFCVMVOBOOPLUBTBM 5 ZÐLMÐ QBS¿BDLMBSEBO R1 WF R2 BZO JõBSFUMJ R ise CVOMBSMB[UJõBSFUMJEJS IV 0OPLUBTOEBLJ-RZÑLÑTFSCFTUCSBLMEôOEB q1 I II III q2 IBOHJZÌOEFIBSFLFUFCBöMBS \" # $ % & V 3. \"ZOEÐ[MFNEFCVMVOBOOPLUBTBMR1WFR2 yükleri- q3 nin etkisinde +RZÐLÐ,OPLUBTOEBOTFSCFTUCSB- #VOBHÌSFBZOEÑ[MFNEFLJ* ** *** *7WF7OPLUB- LMEóOEBõFLJMEFLJZËSÐOHFZJJ[MJZPS MBSOOIBOHJTJOEFFMFLUSJLTFMBMBOTGSPMBCJMJS \" * # ** $ *** % *7 & 7 d Od q1 q2 6. &õJULBSFCËMNFMFSMFBZSMNõEÐ[MFNEFOPLUBTBMR1 d WF R2 ZÐLMFSJOJO 1 OPLUBTOEB PMVõUVSEVLMBS FMFL- triksel alan vektörü E EJS q1 K +q #VOBHÌSF P E * R1 R2(- ZÐLMÐPMVQ R1R2EJS q2 ** R1(- R2(- ZÐLMÐPMVQ R2R1EJS *** R1 R2 ZÐLMÐPMVQ R1 R2EJS #VOB HÌSF ZÑLMFSJO CÑZÑLMÑLMFSJ PSBO R1 R2 ZBSHMBSOEBOIBOHJMFSJEPôSVPMBCJMJS LBÀUS \" :BMO[* # :BMO[** $ *WF*** % **WF*** & * **WF*** \" # 3 5 $ % & 5 5 1. E 2. A 3. E 15 4. E 5. D 6. E

11. SINIF .0%·- &-&,53÷,4&-,677&5\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr )BZBUN[EB'J[JL &MFLUSPTLPQ #JSV¿BLZMESN¿BSQNBTOEBOOBTMLPSVOVS 6¿BLTFZBIBUMFSJOEFZPMDVMBSODBOHÐWFOMJóJOJTBóMBZBOUFNFMJM- ke BTMOEBCJSGJ[JLZBTBTOEBOCBõLBCJSõFZEFóJMEJS'BSBEBZLBGFTJTBZFTJOEFV¿BLTFZBIBUMFSJOEFZPMDVMBSZM- ESNMBSBLBSõHÐWFOMJCJSZPMDVMVLZBQNBLUBESMBS1FLJ'BSBEBZ,BGFTJOFEJS #JS'BSBEBZLBGFTJHÐ¿MÐFMFLUSJL BMBOMBSWFFMFLUSPNBOZFUJLBMBOMBSEBOLFOEJJ¿IBDNJOJLPSVZBOCJSLBQBMJMFULFOLBCVLUVS ZMOEB.JDIBFM'BSBEBZUBSBGOEBOLFõGFEJMFOCJSPMBZPMBO'BSBEBZLBGFTJCJSFMFLUSJLJMFULFOJOEFQP[JUJGWF- ZBOFHBUJGPMBOUÐNGB[MBZÐLMFSJOJMFULFOJOZÐ[FZJÐ[FSJOEFEFOHFEFCVMVONBTWFZÐ[FZEFCJSJLFOZÐLMFSJOLÐSF- TFMTJNFUSJFULJTJOEFOEPMBZJMFULFOJOJ¿IBDNJOEFFMFLUSJLBMBOTGSMBNBTES 'BSBEBZLBGFTMFSJOJOCFMLJEFFO¿BSQDVZHVMBNBTZMESN¿BSQNBMBSOBLBSõTBóMBEóLPSVNBES&óFSZME- SN¿BSQNBTNFUBMCJSLBQBMV¿BóWFZBBSBCBZFULJMFSTFJ¿JOEFLJJOTBOMBSNFUBMJLZÐ[FZJOEõFMFLUSJLTFMPMBSBL CJSUFNBTBHJSNFEJLMFSJTÐSFDFHÐWFOEFLBMBDBLMBSES,BQBMNFUBMJLBSB¿WFZBV¿BLCJS'BSBEBZLBGFTJHJCJEBW- SBOSWFZMESNOHÐ¿MÐFMFLUSJLBMBOOEBOJ¿LTNLPSVONVõPMVS .JDIBFM'BSBEBZ - &ZMÐMEF-POESBZBLOMBSOEBLJ/FXJOHUPO#VUUTLBTBCBTOEBEPóBO'BSBEBZhO ¿PDVLMVóVZPLTVMMVLJ¿JOEFHF¿NJõUJSZBõOEBNBUCBBMBSEBDJMU¿J¿SBLMóOBCBõMBZBO 'BSBEBZ DJMUMFEJóJLJUBQMBSEBOË[FMMJLMFCJMJNTFMPMBOMBSCÐZÐLCJSUVULVJMFPLVNVõ FMFLUSJL WFLJNZBZBPMBOJMHJTJWFCJMHJTJHJEFSFLBSUNõUSEFLJNZBD)%\"7: 'BSBEBZBTJT- UBOMóBLBCVMFUNJõUJS\"LEFNJLHËSFWFCBõMBZBO'BSBEBZJMLPMBSBLNBOZFUJLBMBOEBJ¿JO- EFOBLNHF¿FOCJSUFMJOIBSFLFULB[BOEóO CËZMFDFFMFLUSJLFOFSKJTJOJONFLBOJLFOFSKJ- ZF EËOÐõUÐóÐOÐ PSUBZB LPZBSBL FMFLUSJL NPUPSMBSOO QSFOTJQMFSJOJ LFõGFUNJõUJS #VOEBOTPOSBZMLJNZBJMFVóSBõBSBLCFO[FOWFCÐUJMFOJ LFõGFUNJõ JMLEFGBQBTMBONB[ ¿FMJóJJNBMFUNJõ LMPSWFEJóFSHB[MBSTWMBõUSNõUShEFFMFLUSPNBOZFUJLJOEÐLTJZPOPMBZOLFõGFEFSFLNF- LBOJLFOFSKJOJOFMFLUSJLFOFSKJTJOFEËOÐõUÐSÐMFCJMFDFóJOJHËTUFSNJõUJS &MFLUSJLTFMBMBOLVWWFU¿J[HJMFSJLBWSBNOPSUBZBBUBSBLFMFLUSJLWFNBOZFUJLBMBOOË[FMMJLMFSJOJB¿LMBZBO GJ[JLUF FOCÐZÐLEFOFZDJWFZBSBUDPMBSBLUBOOBONBUFNBUJLCJMNFEJóJIBMEF¿PLËOFNMJUFPSJLHËSÐõMFSEFPSUBZBLPZBO 'BSBEBZ\"óVTUPThEFIBZBUBHË[MFSJOJZVNNVõUVS 16

&-&,53÷,4&-,677&57&&-&,53÷,\"-\"/ KARMA TEST - 1 1. ôFLJMEFLJBZOEPóSVMUVÐ[FSJOEFCVMVOBOOPLUBTBM 4. ôFLJMEFWFSJMFOOPLUBTBMZÐLMFSEFO+ROVO2ZBVZ- R1 R2 ve R ZÐLMFSJOEFO R1 JO R2 ZF VZHVMBEó HVMBEóFMFLUSJLTFMLVWWFUJOCÐZÐLMÐóÐ'UJS kuvvet F UJS +q q1 = –q q2 = +q q3 = +9q +8q d 3d 2d Q d 3d #VOBHÌSF R3ÑO R2 ye VZHVMBEôLVWWFULBÀ –9q ' PMVS #VOB HÌSF 2 ZB FULJ FEFO CJMFöLF FMFLUSJLTFM \" # m $ % m & 1 LVWWFUJOCÑZÑLMÑôÑLBÀ'PMVS 2 1 \" # $ 2 % 2 2 & 2 2. \"ZOEÐ[MFNEFCVMVOBOõFLJMEFLJOPLUBTBMR1WFR2 5. ôFLJMEFLJHJCJJ¿J¿FLPONVõFõNFSLF[MJLÐSFMFSEFO yüklerinin +R ZÐLÐOF VZHVMBELMBS CJMFõLF kuvvet J¿UFLJ+R EõUBLJ+RZÐLMÐEÐS,OPLUBTOEBLJ FMFLUSJLTFMBMBOOCÐZÐLMÐóÐ&K, L deki ise ELEJS F UJS +2q q1 +q q2 F +q K rL rr #VOBHÌSF q1 PSBOLBÀUS #VOBHÌSF EK PSBOLBÀUS q2 EL \" # m $ m % & \" # 3 $ % 5 & 2 2 3. ôFLJMEFLJTÐSUÐONFTJ[ZBMULBO[FNJOÐ[FSJOEFCV- lunan noktasal +R WF +R ZÐLMFSJOJO TBCJU +R ZÐLÐOFV[BLMLMBSEWFELBEBSES ** *** 6. \"ZOEÐ[MFNEFCVMVOBO-R +RWFR9 noktasal * *7 7 ZÐLMFSJOJO 0 OPLUBTOEB PMVõUVSEVóV CJMFõLF FMFL- trik alan E õFLJMEFLJHJCJEJS +3q d qx +q 2d O E +16q –q +2q #VOBHÌSF +RZÑLÑOFVZHVMBOBOCJMFöLFLVW- #VOBHÌSFRXZÑLÑOFE JS WFUJOZÌOÑPLMBSMBHÌTUFSJMFOZÌOMFSEFOIBOHJTJ PMVS \" mR # mR $ +R \" * # ** $ *** % *7 & 7 % +R & +R 1. A 2. C 3. B 17 4. D 5. E 6. C

KARMA TEST - 2 &-&,53÷,4&-,677&57&&-&,53÷,\"-\"/ 1. öMFULFO +R ZÐLMÐ , LÐSFTJOJO 0 OPLUBTOEB PMVõ 3. ôFLJMEFLJ,-.JLJ[LFOBSEJLÐ¿HFOJOJO, -WF. UVSEVóVFMFLUSJLTFMBMBOõFLJM-*EFLJHJCJEJS LËõFMFSJOFTSBTZMB+R R1WFR2ZÐLMFSJLPONVõ UVS#VZÐLMFSJOõFLJMEFLJ0OPLUBTOEBPMVõUVSEVóV +q E L elektriksel alan vektörü E EJS KO VI K +q II +q KO OE III ôFLJMm* IV ôFLJMm** ÷MFULFO OÌUS WF , ZB Ì[EFö - LÑSFTJ , ZB EP LM LVOEVSVMVQöFLJM-II deki yerine konduktan son- q1 q2 SB0OPLUBTOEBPMVöBOCJMFöLFFMFLUSJLTFMBMBO öFLJM-**EFHÌTUFSJMFOMFSEFOIBOHJTJEJS #VOBHÌSFR2ZÑLÑLBÀREVS #JSJNLBSFMFSÌ[EFõUJS \" 1 # 1 $ % & 4 2 \" * # ** $ *** % *7 & 7 4. &MFLUSJLBMBOJMFJMHJMJ * &MFLUSJLBMBOOEBLVWWFU¿J[HJMFSJBMBOWFLUËSÐ- OFEJLUJS ** &MFLUSJLBMBOJ¿JOEFCVMVOBOCJSRZÐLÐOFFULJ FEFOLVWWFUJOZËOÐ ZÐL JTF&JMFBZOZËO- MÐ m JTFUFSTZËOMÐEÐS 2. R1ZÐLÐOÐO,OPLUBTOEBPMVõUVSEVóVFMFLUSJLTFM *** &MFLUSJL BMBO WFLUËSFM CJS CÐZÐLMÐLUÐS :ËOÐ m ZÐLMFSEF EõBSEBO ZÐLF ZÐLMFSEF ZÐL- BMBOõFLJM-I deki E1 LBEBSES UFOEõBSZBEPóSVEVS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[* # :BMO[** $ *WF** % **WF*** & * **WF*** q1 K E1 q1 K q2 E2 5. \"ZOEÐ[MFNEFCVMVO BO+R Rx ve +RZÐLMFSJOJOLP- ôFLJMm** ôFLJMm* OVNMBSõFLJME FLJHJCJEJS O q1 ve q2ZÑLMÑDJTJNMFSJOöFLJM-**EFLJLPöVM 2a a 2a MBSEB PMVöUVSE VôV CJMFöLF FMFLUSJLTFM BMBO E2 PMEVôVOBHÌSF * R1ZÐLÐ JõBSFUMJEJS +q qX +q ** R2ZÐLÐ m JõBSFUMJEJS *** R1WFR2ZÐLMFSJOJOCÐZÐLMÐóÐBZOES :ÑLMFSJO 0 OPLUBT OEB PMVöUVSEVLMBS CJMFöLF ZBSHMBSOEBOIBOHJMFSJEPôSVEVS FMFLUSJLT FMBMBOTGSPME VôVOBHÌSFRXZÑLÑLBÀ REVS #JSJNLBSFMFSÌ[EFõUJS \" :BMO[* # :BMO[*** $ *WF** \" - 1 # - 1 $ % 1 & - 3 42 24 % **WF*** & * **WF*** 1. C 2. E 18 3. C 4. D 5. A

&-&,53÷,4&-,677&57&&-&,53÷,\"-\"/ KARMA TEST - 3 1. ôFLJMEFLJ FõLFOBS Ð¿HFOJO LËõFMFSJOF ZFSMFõUJSJMFO 4. \"ZOEÐ[MFNEFCVMVOBOR1WFR2 yüklerinin +RZÐ- K deki -RZÐLÐOÐO0EBPMVõUVSEVóVFMFLUSJLBMBO LÐOFVZHVMBELMBSCJMFõLFkuvvet F õFLJMEFLJHJCJ- õJEEFUJ&EJS EJS K mR F q1 +q O +2q L M mR #VOBHÌSF 0EBLJCJMFöLFFMFLUSJLTFMBMBOöJE- q2 EFUJLBÀ&PMVS \" E # & $ 3E % & & 5E #VOBHÌSF q1 PSBOLBÀUS 2 22 q2 \" - 2 9 3 % – 3 & 9 # $ 2 2 2 2. ôFLJMEFLJTÐSUÐONFTJ[ZBMULBOFóJLEÐ[MFNEFCV- MVOBOR9 ve R:ZÐLMÐLÐSFMFSEFOHFEFEJS5JQHFSJM- me kuvveti NHEJS T qY Y qX X 30° :DJTNJOJOLÑUMFTJNPMEVôVOBHÌSF 9DJTNJ- OJOLÑUMFTJLBÀNEJS (sin 30° = 1 , cos 30° = 3 H=ZFS¿FLJNJJWNFTJ 5. ôFLJMEF WFSJMFO FõLFOBS Ð¿HFOJO LËõFMFSJOEFLJ 22 noktasal +R +RWF–RZÐLMFSJOEFO+ROVO–RZÐ- \" N # N $ N % N & m LÐOF VZHVMBEó FMFLUSJLTFM LVWWFUJO CÐZÐLMÐóÐ ' 2 EJS 3. ôFLJMEF BZO EPóSVMUV Ð[FSJOEF CVMVOBO OPLUBTBM +2q R1 R2WFRZÐLMFSJOEFORZÐLÐOFFULJFEFOCJMFõ- dd LFLVWWFUTGSESR1 = –REVS q1 +q q2 mR +q d 2d d #VOBHÌSF R2ZÑLÑLBÀREVS #VOBHÌSF RZÑLÑOFFULJFEFOCJMFöLFFMFL- USJLTFMLVWWFUJOCÑZÑLMÑôÑLBÀ'EJS \" mR # +R $ mR % mR & +R \" # $ % 2 3 & 1. D 2. A 3. D 19 4. B 5. C

KARMA TEST - 4 &-&,53÷,4&-,677&57&&-&,53÷,\"-\"/ 1. ôFLJMEFLJ 0 OPLUBTOEB CVMVOBO +R ZÐLMÐ DJTNF 4. ôFLJMEF FõJU V[VOMVLUBLJ ZBMULBO JQMFSF BTM 9 WF R1 WFR2ZÐLMFSJOJOVZHVMBEóLVWWFUMFSJOCJMFõLFTJ : ZÐLMÐ LÐSFMFSJOJO CBóM PMEVóV JQMFSEFLJ HFSJMNF LVWWFUMFSJFõJUCÐZÐLMÐLUFEJS F PMBSBLWFSJMNJõUJS F öQ a b öQ q1 O +q q2 XY #VOBHÌSF q1 PSBOLBÀUS #VOBHÌSF q2 * $JTJNMFSJOZÐLCÐZÐLMÐLMFSJFõJUUJS ** a ve bB¿MBSFõJUUJS \" 4 # m $ % 1 & 9 9 34 *** 9WF:DJTJNMFSJOJOLÐUMFMFSJFõJUUJS 2. ôFLJMEFLJ+RZÐLÐOFR1WFR2ZÐLMFSJOJOVZHVMBEó ZBSHMBSOEBOIBOHJMFSJkesinlikleEPôSVEVS CJMFõLFLVWWFU F EJS \" :BMO[* # :BMO[** $ :BMO[*** % *WF*** & **WF*** +q F q1 q2 #VOBHÌSFZÑLMFSJOPSBO q1 LBÀUS q2 #JSJNLBSFMFSÌ[EFõ \" 1 # 1 $ % - 1 & - 1 5. ôFLJMEF, -WF.ZÐLMÐDJTJNMFSJOBSBTOEBLJFMFL- 4 2 24 USJLBMBO¿J[HJMFSJWFSJMNJõUJS 3. %ÐõFZEÐ[MFNEFZBMULBOJQMFSMFBTMPMBONLÐUMF- K LM MJ R ZÐLMÐ Ë[EFõ 9 WF : DJTJNMFSJ EFOHFEFZLFO 41 JQJOEFNFZEBOBHFMFOHFSJMNFLVWWFUJOJOCÐZÐLMÐ- óÐ51, S2JQJOEFLJOJOJTF52EJS S1 JQJ X S2 JQJ #VOBHÌSF , -WF.OJOZÑLJöBSFUMFSJOBTMES Y K L . A) – – – 9JMF:BSBTOEBPMVöBOFMFLUSJLTFMLVWWFUJOCÑ- B) + + + ZÑLMÑôÑNHLBEBSPMEVôVOBHÌSF 5152JQHF- C) + – – SJMNFMFSJPSBOLBÀUS D) + + – E) – + – \" # $ % 1 & 1 24 1. E 2. E 3. C 4. E 5. C

&-&,53÷,4&-,677&57&&-&,53÷,\"-\"/ YAZILI SORULARI 1. #JSLFOBSNPMBOFõLFOBSÐ¿HFOJOLËõFMFSJOFõF- 3. ôFLJMEFLJ 9 OPLUBTOB OPLUBTBM CJS 2 ZÐLÐ LPOVM- LJMEFLJHJCJOPLUBTBMR9 R:WFR;ZÐLMFSJLPOVMVZPS NVõUVS #V ZÐLÐO ; OPLUBTOEB PMVõUVSEVóV FMFL- qX = 3.10–5C USJLBMBOõJEEFUJ/$EVS Q XY ZT qY = 3.10–5C qZ = 2.10–4C /PLUBMBSBSBTV[BLMLMBSFöJUPMEVôVOBHÌSF : WF 5 OPLUBMBSOEBLJ FMFLUSJL BMBO öJEEFUMFSJ LBÀ qZZÑLÑOFFULJFEFOCJMFöLFLVWWFULBÀ/EVS /DPMVS f k = 9.109 Nm2 p k.Q E= k.Q = 72 N/C 18 = N/C C2 Y2 2 d qX 4d E= k.Q =8 60° kQ 9.109.6.10–9 T2 FXZ = 9 = 6 = 72 gd 2 d FYZ = 9.109.6.10–9 = 6 9 FXZ = 6 4. \"ZOEÐ[MFNEFCVMVOBOWFZÐLMFSJR9 =μC ve qY qZ 60° R: =μ$PMBOOPLUBTBMDJTJNMFSõFLJMEFLJHJCJ, R=6 3N OPLUBTOEBO TSBTZMB N WF N V[BLMóB ZFSMFõUJ- FXZ = 6 SJMNJõMFSEJS 3nC K 3m 2. 6[VOMVóVNPMBOZBMULBOJQJOVDVOBLÐUMFTJLH X ZÐLÐRPMBOJLJDJTJNCBóMBOQõFLJMEFLJHJCJBTME- 6m óOEBEFOHFEFLBMZPSMBS 5 m 53° 53° 5 m 16nC Y F 4m 4m qq #VOBHÌSF 9WF:ZÑLMFSJOJO,OPLUBTOEBPMVö- mg UVSEVLMBSCJMFöLFFMFLUSJLTFMBMBOLBÀ/$PMVS f 1nC = 10–6C, k = 9.109 Na2 p C2 #VOBHÌSF RZÑLÑLBÀ$PVMPNCEVS 3.10–6C EY ECJMFöLF X 3m EX f k = 9.109 Nm2 p C2 F 6m tan 53° = mg F = 40 N 4F = 16.10–6C 3 30 Y q .q 9 –6 12 9.10 .3.10 E= = 3 F = k. X9 ECJMFöLF =3/D 3.10 2 9 –6 d 9.10 .16.10 E= = 3 92 4.10 9.10 .q 40 = 64 16 –8 q = .10 c 3 Y 36 1. 6 3 16 - 21 3. EY = 72 NC, ET/$ 4. ECJMFöLF3/$ 2. .10 C 3

YAZILI SORULARI &-&,53÷,4&-,677&57&&-&,53÷,\"-\"/ 5. ôFLJMEFLJCJSZBS¿BQM¿FNCFSJO9 :WF;OPLUBMB- 7. \"óSMLMBSTSBTZMB(WF(PMBOZÐLMÐ9WF:DJ- SOBTSBZMB-R -RWF 2 q noktasal yükleri konul- TJNMFSJEÐõFZEÐ[MFNEFõFLJMEFLJHJCJEFOHFEFEJS NVõUVS +q 2 F EK X r G d E E mR E2 Y ZFS mR 2G F K #VOB HÌSF ÀFNCFSJO NFSLF[JOEFLJ CJMFöLF #VOB HÌSF : DJTNJOJO ZFSF VZHVMBEô UFQLJ FMFLUSJLBMBOOOTGSPMBCJMNFTJJÀJO,OPLUBT- LVWWFUJLBÀ(PMVS OBLPOVMNBTHFSFLFOZÑLLBÀRPMNBMES 9JOEFOHFEFLBMNBTJÀJO'=(PMNBMES EK 4GSPMNBTJÀJO N = Tepki kuvveti N = F + 2G 2E 2 EK = 2E 2 N = 3G #VEVSVNEB Y q = 2 2 qPMNBMES ZFS EE K F 2G E2 8. \"ZO EÐ[MFNEF õFLJMEFLJ HJCJ ZFSMFõUJSJMNJõ PMBO OPLUBTBMZÐLMFSJO0EBPMVõUVSEVóVCJMFõLFFMFLUSJL- TFMBMBOOõJEEFUJ&EJS +q x y mR 6. ôFLJMEFLJ(BóSMLMË[EFõZÐLMÐ,WF-LÐSFMFSJEÐ- E' 60° õFZLFTJUJWFSJMFOTÐSUÐONFTJ[FóJLEÐ[MFNÐ[FSJO- 60° 60° EFEFOHFEFEJS mR E' E' 60° +q E' O T F L 9 WF : LÑSFMFSJ LFOEJ BSBMBSOEB ZFS EFôJöUJSJS- F TF 0 EBLJ CJMFöLF FMFLUSJL BMBOO öJEEFUJ LBÀ & G.sin30° PMVS K G.sin30° 30° %VSVN %VSVN Eh = 2E E' #VOBHÌSF JQUFPMVöBO5JQHFSJMNFTJLBÀ(EJS E' 3E' 120° 3E' = 3(2E)=6E '=(TJO 5='+(TJO G E' GG T=G F= T= + E' 2 22 5. q = 2 2 q 6. 5( 22 7. ( 8. 6E K

&-&,53÷,4&-,677&57&&-&,53÷,\"-\"/ <(1m1(6m/6258/$5 1. #BIBSËóSFUNFOWFËóSFODJMFSJGJ[JLMBCPSBUVWBSO- 2. #JSGJ[JLËóSFUNFOJTOGBBõBóEBLJEFOFZEÐ[FOF- EBFMFLUSJLTFMLVWWFUEFOFZJJ¿JOBõBóEBLJEÐ[FOF- óJOJIB[SMBZBSBLHJSJZPS óJIB[SMZPSMBS ø ab ø q1 K q L %ÐõFZ q2 ²ôSFODJMFSJOF FöJUCPZEBLJZBMULBOJQMFSJOVDV- OBBTUôJMFULFOZÑLMÑLÑSFMFSJOEFOHFEFPMEV- 4ÐSUÐONFTJ[ ZBUBZ ZBMULBO NBTB Ð[FSJOEF CVMV- ôVOVTÌZMFZFOÌôSFUNFO JQMFSJOEÑöFZEFZBQ- nan +ZÐLMÐOPLUBTBMR1WFR2ZÐLMFSJTBCJUUJS#B- UôBÀMBSOOFEFOFöJUPMNBEôOTPSEVôVOEB IBSËóSFUNFOËóSFODJMFSF,OPLUBTOBCSBLMBO+R ZÐLMÐCJSDJTNJOEFOHFEFLBMEóOHËTUFSJZPS õFZEB Z,ÐSFMFSJOZÐLNJLUBSMBSGBSLMES $JTNJ-ZFLPZBSTBNZJOFEFOHFEFLBMS 4JNHF Z,ÐSFMFSJOLÐUMFMFSJGBSLMES )BZEBS ,V[FZ Z,ÐSFMFSJOCJSCJSJOFVZHVMBEóFMFLUSJLTFM LVWWFUMFSJOCÐZÐLMÐLMFSJBZOES $JTNJ-ZFLPZBSTBN,ZFEPóSVI[MBOS 4JOBO 4F[FS ZöQMFSJOCPZMBSFõJUUJS q2OJOVZHVMBEóFMFLUSJLTFMLVWWFU #BöBL Z,ÐSFMFSJOCÐZÐLMÐLMFSJJMFJMHJMJCJMHJNJ[PM- EPLV[LBUOB¿LBS NBEóJ¿JOZPSVNZBQMBNB[ \"INFU #VOBHÌSF IBOHJÌôSFODJMFSJOTÌZMFEJLMFSJJGBEF $FWBQMBSO WFSFO ÌôSFODJMFSEFO IBOHJTJOJO MFSEPôSVEVS TÌZMFEJôJEPôSVPMVS \" :BMO[)BZEBS # :BMO[4JOBO \" ôFZEB # 4JNHF $ ,V[FZ $ Haydar ve Sinan % )BZEBSWF\"INFU % 4F[FS & #BõBL & 4JOBOWF\"INFU 1. E 23 2. B

<(1m1(6m/6258/$5 &-&,53÷,4&-,677&57&&-&,53÷,\"-\"/ 1. Bilgi::ÐLMÐJMFULFONFUBMLÐSFOJOJ¿JOEFFMFLUSJLTFM 3. 4OGUBQSPKFLTJZPOZBSENZMBUBIUBZBBõBóEBLJTJ- BMBOõJEEFUJTGSES NÐMBTZPOVZBOTUBOËóSFUNFO ËóSFODJMFSJOEFOZP- SVNZBQNBMBSOJTUJZPS :BóNVSMVIBWBMBSEBZMESNEÐõNF UFIMJLFTJOFLBSõOBSB¿UBOEõBS ¿LNBNBMZ[ .VTUBGB &WWFJõZFSMFSJOEFUPQSBLMBNBM X d1 d2 Y TJTUFNMFSLVMMBONBMZ[ O ,FNBM &MFLUSPOJLEFWSFFMFNBOMBSOEõ FMFLUSJLBMBOEBOLPSVNBLJ¿JOJ¿ZÐ[FZJ ZBMUMNõNFUBMLVUVLVMMBONBMZ[ \"UB #VOBHÌSF IBOHJÌôSFODJMFSJOWFSEJôJÌSOFLMFS ZVLBSEBLJCJMHJZJEPôSVMBSOJUFMJLUFEJS \" :BMO[\"UB # :BMO[.VTUBGB Can: 9WF:LÐSFMFSJ - JõBSFUMJEJS $ :BMO[,FNBM % .VTUBGBWF\"UB 4FSEBS9JOZÐLNJLUBS:OJOZÐLNJLUBSOEBOGB[- MBES & ,FNBMWF\"UB Esin:0OPLUBTOEBLJFMFLUSJLBMBOTGSES #VOBHÌSF IBOHJÌôSFODJMFSJOZBQUôZPSVNMBS kesinlikleEPôSVEVS 2. &MFLUSJL BMBO ÐOJUFTJOEF ËóSFUNFO ËóSFODJMFSF LP- \" :BMO[$BO # :BMO[&TJO OVZV BOMBUULUBO TPOSB BõBóEBLJ õFLJMMFSJ UBIUB- $ 4FSEBSWF&TJO % $BOWF4FSEBS ZB ¿J[JQ ËóSFODJMFSJO EFóFSMFOEJSNFMFS ZBQNBTO CFLMFNFLUFEJS & $BO 4FSEBSWF&TJO 9JOZÐL XY &MFLUSJL NJLUBS BMBO¿J[ :OJO 9DJTNJQP[JUJGZÐLMÐ HJMFSJZÐ ZÐLNJL :DJTNJOFHBUJG [FZMFSF UBSOEBO ZÐLMÐEÐS EJLUJS GB[MBES 0TNBO &GF .JOB #VOB HÌSF ÌôSFODJMFSEFO IBOHJTJOJO DFWBC EPôSVEVS \" :BMO[&GF # :BMO[.JOB $ :BMO[0TNBO % &GFWF.JOB & &GFWF0TNBO 1. D 2. E 24 3. A

ELEKTRİKSEL POTANSİYEL ³ Elektriksel Potansiyel • 26 ³ Konu Testleri • 32 ³ Elektriksel Potansiyel Farkı ve Elektriksel İş • 34 ³ Konu Testleri • 38 ³ Karma Testler • 41 ³ Yazılı Soruları • 46 ³ Yeni Nesil Sorular • 48

11. SINIF 5. MODÜL &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr &MFLUSJLTFM1PUBOTJZFM ÷MJöLJMJ,B[BONMBS 11.2.2.1. : /PLUBTBMZÐLMFSJ¿JOFMFLUSJLTFMQPUBOTJZFMFOFSKJ FMFLUSJLTFMQPUBOTJZFM FMFLUSJLTFMQPUBOTJZFMGBSLWFFMFLUSJLTFMJõ LBWSBNMBSOB¿LMBS /PLUBTBM:ÑLMFS÷ÀJO&MFLUSJLTFM1PUBOTJZFM&OFSKJ %m/*m Yatay bir zemin üzerinde duran bir cismi yerden belli bir yük- &MFLUSJLTFM,VWWFU ' TFLMJóF¿LBSUNBLJ¿JOZFS¿FLJNJLVWWFUJOFLBSõJõZBQMS 4VZÐ[FZJOEFEVSBOQMBTUJLUPQVCFMMJCJSEFSJOMJóFEBMES- F NBLJ¿JOTVZVOLBMESNBLVWWFUJOFLBSõJõZBQMS #JSZBZTLõUSNBLJ¿JOZBZÐ[FSJOEFJõZBQMS 8&P 6[BLML E E Þ :VLBSEBLJ IFS Ð¿ ËSOFLUF PSUBL PMBO õFZ CJS LVWWFUF LBSõ Jõ ZBQMEó [BNBO ZBQMBO JõJO QPUBOTJZFM FOFSKJ \"WF#OPLUBMBSOEBTBCJUUVUVMBOZÐLMFSEFO PMBSBL EFQPMBONBTES #FMMJ CJS ZÐLTFLMJóF ¿LBSMBO DJ- +q2 ZÐLÐ TFSCFTU CSBLMEóOEB CV ZÐLMFSJO TJN TV J¿JOF EBMESMBO UPQ TLõUSMBO ZBZ TFSCFTU C- CJSCJSMFSJOF VZHVMBELMBS FMFLUSJLTFM LVWWFUJO SBLMELMBSOEBIBSFLFUFHF¿FS:BQMBOJõMFS QPUBOTJZFM V[BLMóBCBóMHSBGJóJZVLBSEBLJHJCJPMVS,VW- FOFSKJ PMBSBL EFQPMBOSLFO DJTJNMFS TFSCFTU CSBLMELMB- WFU-V[BLML HSBGJóJOJO BMUOEB LBMBO BMBO LVW- SOEBEFQPMBOBOQPUBOTJZFMFOFSKJZJIBSDBZBSBLIBSFLFU WFUJO ZBQUó JõJ WFSJS :VLBSEBLJ HSBGJLUF CV FOFSKJTJLB[BOSMBS alan k· q1·q2 PMVS (SBGJóJO BMUOEBLJ BMBO d F CV HSBGJóJO EFOLMFNJOJO JOUFHSBMJ BMOBSBL IF- TBQMBOS F F #VOBHËSF+q2ZÐLÐOÐ#OPLUBTOEBOTPOTV- [BHËUÐSNFLJ¿JOZBQMBOJõ k· q1·q2 kadar- #FMMJCJSZÐLTFLMJóF¿- #FMMJCJSEFSJOMJóFEBM- #FMMJCJSNJLUBSTLõU- d LBSMNBLJTUFOFOUPQ ESMNBLJTUFOFOUPQ SMBOZBZ ES#VEVSVNEBZÐLMFSJOTBIJQPMEVóVFMFLUSJL- TFMQPUBOTJZFMFOFSKJ TANIM +q1 E +q2 TPOTV[ AB :VLBSEBLJõFLJMEFLJHJCJ+q1 yükü sabit tutu- EP = k· q1·q2 MVQ +q2 ZÐLÐ TPOTV[EBO # OPLUBTOB HFUJ- d SJMJSLFOCJSJõZBQMS#VJõZBZTLõUSNBLJ¿JO CBóOUTJMFIFTBQMBOS ZBQMBO JõF CFO[FS :ÐLMFS BZO JõBSFUMJ PMEVóV 1PUBOTJZFMFOFSKJOJOCJSJNJiKPVMFuEÐSWFTLBMFS J¿JO CJSCJSMFSJOJ FMFLUSJLTFM LVWWFUMF JUFS :ÐLMFSJ CJSCÐZÐLMÐLUÐS1PUBOTJZFMFOFSKJTLBMFSCJSCÐ- ZÐLMÐLPMEVóVJ¿JOIFTBQMBNBMBSEBZÐLMFS JõB- CJSCJSJOF ZBLMBõUSNBL J¿JO FMFLUSJLTFM LVWWFUMF- SFUMFSJJMFCJSMJLUFLVMMBOMS#JSCJSJOJJUFOZÐLMFSJO QPUBOTJZFMFOFSKJMFSJQP[JUJG CJSCJSJOJ¿FLFOZÐL- SFLBSõJõZBQMNBTHFSFLJS:BQMBOCVJõTJT- MFSJOQPUBOTJZFMFOFSKJTJOFHBUJGPMVS UFNEFQPUBOTJZFMFOFSKJPMBSBLEFQPMBOS,TB- ca +q2ZÐLÐOÐTPOTV[EBO#OPLUBTOBTB- CJUI[MBHFUJSNFLJ¿JOFMFLUSJLTFMLVWWFUMFSFLB- õ ZBQMBO Jõ ZÐLMFSJO TBIJQ PMEVóV elektriksel QPUBOTJZFMFOFSKJZJWFSJS 26

www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" 5. MODÜL 11. SINIF ÖRNEK 1 %m/*m \"WF#OPLUBMBSOEBTBCJUUVUVMBO+q yüklerinden B +q1 E2 –q OPLUBTOEBLJZÐL$OPLUBTOBHFUJSJMFSFLCVOPLUBZBTB- CJUMFOJZPS E1 E +q E +q A BC #VOB HÌSF ZÑLMFSJO FMFLUSJLTFM QPUBOTJZFM FOFSKJTJ +q2 OBTMEFôJöJS &MFLUSJLTFM QPUBOTJZFM FOFSKJOJO GPSNÑMÑ EP = k q1q2 /PLUBTBMCJSZÐLÐOFMFLUSJLTFMQPUBOTJZFMFOFS- d KJTJ FUSBGOEBLJ ZÐLMFSEFO LBZOBLMBOS /PLUB- PMEVôVOEBOZVLBSEBLJZÑLMFSJO\"WF#OPLUBMBSOEBZ- TBM ZÐLMFSEFO PMVõBO TJTUFNJO UPQMBN FMFLUSJL- q2 LFO TBIJQ PMEVLMBS FMFLUSJL QPUBOTJZFM FOFSKJMFSJ k TFMQPUBOTJZFMFOFSKJTJ IFSCJSZÐL¿JGUJOJOFMFLU- d LBEBSES'PSNÑMEFOEFBOMBöMBDBôÑ[FSFZÑLMFSBSBTO- SJLTFM QPUBOTJZFM FOFSKJMFSJOJO DFCJSTFM UPQMBN- EBLJ V[BLML BSUUôOEB CV EFôFS B[BMS 4POTV[EB JTF T- GSPMVS OBFõJUUJS#VOBHËSFZVLBSEBLJTJTUFNJOFMFLU- #VOBHÌSFZÑL#OPLUBTOEBO$OPLUBTOBHFUJSJMEJôJO- SJLTFMQPUBOTJZFMFOFSKJTJ EFZÑLMFSBSBTOEBLJV[BLMLBSUUôOEBOTJTUFNJOFMFLUSJL- TFMQPUBOTJZFMFOFSKJTJB[BMS EP = k q1·q2 +k q1·^ -q3 h +k q2·^ -q3 h d1 d2 d3 CBóOUTJMFIFTBQMBOS ÖRNEK 2 .FSLF[MFSJ\"WF#OPLUBMBSOBTBCJUMFONJõJMFULFO, ÖRNEK 3 WF-LÐSFTFMDJTJNMFSJOJOZÐLMFSJWFZBS¿BQMBSTSBTZMB :ÐLMFSJõFLJMEFWFSJMFODJTJNMFSôFLJM-IEFLJLPOVNMBSO- EBUVUVMVSLFOôFLJM-IIEFLJLPOVNBHFUJSJMJZPSMBS +RWF+R SWFSEJS qL = +4q qLR q1R qK = +2q q,R L E E E E , 2r q1R qmR qmR r AB q2R q2R E #VDJTJNMFSIFSIBOHJCJSZÑLLBZCPMNBEBOCJSCJSMF- ôFLJMmI ôFLJMmII SJOFEPLVOEVSVMVQBZOV[BLMôBLPOVMEVôVOEBTJT- UFNJOFMFLUSJLTFMQPUBOTJZFMFOFSKJTJOBTMEFôJöJS #VOB HÌSF TJTUFNJO FMFLUSJLTFM QPUBOTJZFM FOFSKJTJ OBTMEFôJöNJöUJS qq 12 4JTUFNJO JML FMFLUSJLTFM QPUBOTJZFM FOFSKJTJ EP = k 9q 2 d õFLJM-IEFLJTJTUFNJOFMFLUSJLTFMQPUBOTJZFMFOFSKJTJ CBôOUTOEBOZBSBSMBOMBSBL E = k d PMBSBLIFTBQ- k·q · q k·q· (- 2q) k·q · (- 2q) MBOS Pilk EP1 = d + d + 2d ,WF-JMFULFOLÑSFMFSJCJSCJSJOFEPLVOEVSVMBSBLBZOV[BL- k · 2q2 MôB LPOVMEVôVOEB ZÑLMFSJOJ ZBSÀBQMBS PSBOOEB QBZMBöS- =- d MBSf qson = f q1 + q2 p · r1 p r1 + r2 PMBSBLIFTBQMBOS #VOBHÌSFDJTJNMFSJOTPOZÑLMFSJ õFLJM-IIEFLJTJTUFNJOFMFLUSJLTFMQPUBOTJZFMFOFSKJTJJTF k·q · q k·q· (- 2q) k·q · (- 2q) q › = d 3q + 3q n · r = 2q , q›L = d 3q + 3q n · 2r = 4q K r + 2r r + 2r EP2 = d + d + d k · 3q2 PMBSBLIFTBQMBOS =- #VEVSVNEBTJTUFNJOZFOJFMFLUSJLTFMQPUBOTJZFMFOFSKJTJ d EP = k qq CBôOUTOEBO EPson = k 8q 2 PMBSBLIFTBQ- PMBSBLIFTBQMBOS d 12 #VJLJEFôFSCJSCJSJJMFLBSöMBöUSMSTB&11 > E12EJS #VOBHÌSFTJTUFNJOFMFLUSJLTFMQPUBOTJZFMFOFSKJTJB[BMS d MBOS4POWFJMLFMFLUSJLTFMQPUBOTJZFMFOFSKJMFSJLBSöMBöUSM- EôOEB&1JML > E1TPOTPOVDVOBVMBöMS#VOBHÌSFTJTUF- NJOFMFLUSJLTFMQPUBOTJZFMFOFSKJTJB[BMNöUS 1. \"[BMS 2. \"[BMS 27 3. \"[BMS

11. SINIF 5. MODÜL &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr ÖRNEK 4 ÖRNEK 5 ,FOBS V[VOMVóV DN PMBO FõLFOBS Ð¿HFOJO LËõFMF- ôFLJM-IEFLJZÐLTJTUFNJôFLJM-IIEFLJIBMFHFUJSJMJZPS SJOFZÐLMFSJõFLJMEFWFSJMFOR1 R2WFR3 yükleri yer- MFõUJSJMNJõUJS –q qpm$ EE E E –2q –q +q –2q E +q ôFLJMmI ôFLJMmII q1pm$ DN q2mpm$ #VOBHÌSF #VOBHÌSF B ôFLJM-I WF ôFLJM-IIEFLJ - q yükünün elektriksel QPUBOTJZFMFOFSKJMFSJOJLBSõMBõUSO[ B q1ZÐLÐOÐOFMFLUSJLTFMQPUBOTJZFMFOFSKJTJLB¿ +PMVS C ôFLJM-IWFôFLJM-IIEFLJTJTUFNMFSJOFMFLUSJLTFMQP- UBOTJZFMFOFSKJMFSJOJLBSõMBõUSO[ C ZÐLTJTUFNJOJOFMFLUSJLTFMQPUBOTJZFMFOFSKJTJLB¿ B-RZÑLÑOÑOQPUBOTJZFMFOFSKJTJ-RWF+RZÑLMFSJOJO-R +PMVS L=Y9 Nm2$2 ZÑLÑ Ñ[FSJOEF PMVöUVSEVôV FMFLUSJLTFM QPUBOTJZFM FOFSKJ- MFSJOJO DFCJSTFM UPQMBNOB FöJUUJS #VOB HÌSF õFLJM-I WF :ÑLMFSBSBTNFTBGF õFLJM-IIEFLJ -R ZÑLÑOÑO FMFLUSJLTFM QPUBOTJZFM FOFSKJ- E=DN= 2 · 10-1NPMVS TJTSBTJMF BR1 ZÑLÑOÑO FMFLUSJLTFM QPUBOTJZFM FOFSKJTJ R2 WF R3 k·(- q)·(- 2q) k·(- q)·q k·q2 ZÑLMFSJOJOR1ZÑLÑÑ[FSJOEFPMVöUVSEVôVFMFLUSJLTFMQP- EP1 = + = ve UBOTJZFMFOFSKJMFSJODFCJSTFMUPQMBNOBFöJUUJS#VEVSVN- d dd EBR1ZÑLÑOÑOFMFLUSJLTFMQPUBOTJZFMFOFSKJTJ k·(- q)·(- 2q) k·(- q)·q k·q2 EP2 = += d dd EP1 = k·q1 · q2 + k·q ·q CBôOUTJMFIFTBQMBOS PMSMB SBLIFTBQMBOS#VOBHÌSF&11 = E12TPOVDVOBVMBö- d 13 d #VOBHÌSF&Q1 Cõ FLJM-IEFLJ TJTUFNJO FMFLUSJLTFM QPUBOTJZFM FOFSKJTJ IFS CJS ZÑL ÀJGUJOJO FMFLUSJLTFM QPUBOTJZFM FOFSKJMFSJOJO DFCJS- E = 9 ·109 · 4 ·10-6 · (- 3 ·10-6 ) + 9 ·109 · 4 ·10-6 · 6 ·10-6 TFMUPQMBNES#VOBHÌSFõFLJM-IEFLJTJTUFNJOFMFLUSJL- 2 ·10-1 2 ·10-1 TFMQPUBOTJZFMFOFSKJTJ P1 = 0, 54 J olur. k·(- 2q)·q k·(- 2q)·(- q) k·(- q)·q EPtoplam1 = d + + d d C4JTUFNJOFMFLUSJLTFMQPUBOTJZFMFOFSKJTJIFSCJSZÑLÀJGUJ- k·q2 , OJO FMFLUSJLTFM QPUBOTJZFM FOFSKJMFSJOJO DFCJSTFM UPQMBN- = - dir. ES#VOBHÌSFTJTUFNJOFMFLUSJLTFMQPUBOTJZFMFOFSKJTJ d EPtoplam = k·q1·q2 + k·q2·q3 + k·q1·q3 õFLJM-IIEFLJTJTUFNJOFMFLUSJLTFMQPUBOTJZFMFOFSKJTJIFS d d d CJS ZÑL ÀJGUJOJO FMFLUSJLTFM QPUBOTJZFM FOFSKJMFSJOJO DFCJS- TFM UPQMBNES #VOB HÌSF õFLJM-IIEFLJ TJTUFNJO FMFLU- CBôOUTJMFIFTBQMBOS SJLTFMQPUBOTJZFMFOFSKJTJ EPtoplam2 = k·(- 2q)· (- q) k·(- q)·q k·(- 2q)·q ++ #VOBHÌSF&QUPQMBN d d 2d 9·109·4·10-6·(- 3·10-6 ) 9·109·(- 3·10-6)·6·10-6 = 0\\d›r. EPtoplam = 2·10-1 + 2·10-1 #VOBHÌSF&1UPQMBN > E1UPQMBNTPOVDVOBVMBöMS + 9·109·6·10-6·4·10-6 2·10 -1 = - 0, 27 J olur. B 0,54 J Cm + 28 B E11 = E12 C E1UPQMBN > E1UPQMBN

www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" 5. MODÜL 11. SINIF /PLUBTBM:ÑLMFS÷ÀJO&MFLUSJLTFM1PUBOTJZFM ÖRNEK 6 7$1,0%m/*m /PLUBTBM+RWF-RZÐLMFSJõFLJMEFLJHJCJZFSMFõ- +q +q1 UJSJMNJõUJS AE B +12q , L M mR E EE E ôFLJMEF#OPLUBTOEBLJR1ZÐLÐ \"OPLUBTOEBLJ #VOBHÌSF, -WF.OPLUBMBSOOFMFLUSJLTFMQP- RZÐLÐOÐOWBSMóOEBOEPMBZFMFLUSJLTFMQPUBOTJ- UBOTJZFMMFSJOJLBSöMBöUSO[ ZFMFOFSKJZFTBIJQUJSR1ZÐLÐLBMESMQ#OPLUB- TOB$MVLCJSJNZÐLZFSMFõUJSJMFDFLPMVOVSTBCV ²ODFMJLMF, -WF.OPLUBMBSOOFMFLUSJLTFMQPUBOTJZFM- ZÐLÐO TBIJQ PMEVóV FMFLUSJLTFM QPUBOTJZFM FOFSKJZF MFSJOJIFTBQMBZBMN 0OPLUBOOFMFLUSJLTFMQPUBOTJZFMJEFOJS #VOBHÌSFCVOPLUBMBSOFMFLUSJLTFMQPUBOTJZFMMFSJ &MFLUSJLTFMQPUBOTJZFMJOTFNCPMÐi7u birimi ise iWPMUu PMVQFMFLUSJLTFMQPUBOTJZFMTLBMFSCJSCÐZÐLMÐLUÐS k·12q k (- 60q) - 8kq V = + = d 3d d K +q $ k·12q k (- 60q) - 24kq VL = 2d + 2d = d k·12q k (- 60q) - 56kq VM = 3d + = AE B d d PMBSBLIFTBQMBOS #BõLBCJSJGBEFJMFFMFLUSJLTFMQPUBOTJZFMi$MVL &MFLUSJLTFMQPUBOTJZFMTLBMFSCJSCÑZÑLMÑLPMEVôVOEBO, CJSJN ZÐLÐ TPOTV[EBO # OPLUBTOB HFUJSNFL J¿JO -WF.OPLUBMBSOOFMFLUSJLTFMQPUBOTJZFMMFSJBSBTOEBLJ ZBQMBOJõUJSuõFLMJOEFB¿LMBOBCJMJS EPôSVTSBMBNB7K >7L >7MöFLMJOEFPMVS #V ZBQMBO B¿LMBNBMBS EPóSVMUVTVOEB FMFLUSJLTFM ÖRNEK 7 QPUBOTJZFM V = EP = k·q·q1 /PLUBTBMR1 R2WFR3ZÐLMFSJ LFOBSV[VOMVLMBSN q1 d WF N PMBO CJS EJLEËSUHFOJO LËõFMFSJOF õFLJMEFLJ HJCJ q1 ZFSMFõUJSJMNJõUJS q1$ qm$ k·q d1= V= d CBóOUTJMFIFTBQMBOS 3 2 3m + 4 2 NE = 5m %m/*m E2N A #JSOPLUBOOFMFLUSJLTFMQPUBOTJZFMJ FUSBGOEBLJ q2$ ZÐLMFSJO P OPLUBEB PMVõUVSEVóV FMFLUSJLTFM QP- UBOTJZFMMFSJODFCJSTFMUPQMBNOBFõJUUJS #VOBHÌSFCVÑÀZÑLÑO\"OPLUBTOEBPMVöUVSEVôV FMFLUSJLTFMQPUBOTJZFMLBÀ7EJS L=p9 Nm2$2 +q1 \"OPLUBTOOFMFLUSJLTFMQPUBOTJZFMJ E E1 V = k·q1 + k·q2 + k·q3 ba€ ›nt›s› kullan›larak d1 d2 d3 A –q2 E2 A VA = 9·109· 15 + 9·109 12 + 9·109 (- 3) 5 4 3 #VOBHËSFõFLJMEFJLJZÐLUFOPMVõBOZÐLTJTUF- NJOEF\"OPLUBTOOFMFLUSJLTFMQPUBOTJZFMJ = 45·109 V olarak hesaplan›r. VA = k·q1 + k·(- q2) Simülasyonu var! d1 d2 &MFLUSJLTFM QPUBOTJZFMJO CBóM PMEV- CBóOUTJMFIFTBQMBOS óVEFóJõLFOMFSJEBIBJZJBOBMJ[FUNFL J¿JOZBOEBLJ2SLPEVJMFWFSJMFOTJNÐ- MBTZPOVLVMMBOBCJMJSTJOJ[ 29 6. 7K7L7M 7. 45 · 1097

11. SINIF 5. MODÜL &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" www.aydinyayinlari.com.tr :ÑLMÑ ÷MFULFO,ÑSFOJO&MFLUSJLTFM1PUBOTJZFMJ ÖRNEK 8 %m/*m -RZÐLMÐJMFULFOCJSLÐSFOJO, -WF.OPLUBMBSOEB PMVõUVSEVóV FMFLUSJLTFM QPUBOTJZFMMFS TSBTZMB 7, 7- + WF7MLBEBSES + +q –q + –– +r – – r M O, L M E – O, L – rr + 22 + – + – + #VOBHÌSFCVOPLUBMBSOFMFLUSJLTFMQPUBOTJZFMMFSJOJ ö¿JEPMVZBEBCPõRZÐLMÐ SZBS¿BQMCJSJMFU- LBSöMBöUSO[ LFOLÐSFOJOJ¿JOEFCVMVOBOCÐUÐOOPLUBMBSEBLJ FMFLUSJLTFM QPUBOTJZFM EFóFSMFSJ LÐSFOJO ZÐ[F- ²ODFMJLMF, -WF.OPLUBMBSOOFMFLUSJLTFMQPUBOTJZFM- ZJOEFLJFMFLUSJLTFMQPUBOTJZFMEFóFSJOFFõJUUJS MFSJOJIFTBQMBZBMN #VOBHËSFCVOPLUBMBSOFMFLUSJLTFMQPUBOTJZFM- ,WF-OPLUBMBSOOFMFLUSJLTFMQPUBOTJZFMMFSJIFTBQMBOS- leri k·q LFO k·q CBôOUTOEBEZFSJOFLÑSFOJOZBSÀBQBMOS 7O =7, =7- = r d CBóOUTJMFIFTBQMBOS .OPLUBTJMFULFOLÑSFOJOEöOEBPMEVôVOEBOCVOPLUB- ,ÐSFOJOEõOEBWFNFSLF[JOEFOELBEBS V[BLMLUBPMBO.OPLUBTOOQPUBOTJZFMJJTF OO FMFLUSJLTFM QPUBOTJZFMJ IFTBQMBOSLFO E ZFSJOF LÑSF- k·q VM = d OJONFSLF[JOEFOCVOPLUBZBPMBOSV[BLMôBMOS CBóOUTJMFIFTBQMBOS #VOBHÌSF &MFLUSJLTFM QPUBOTJZFMJO LÐSF NFSLF[JOEFO V = - k·q V[BLMóB E CBóMEFóJõJNHSBGJóJBõBóEBWF- SJMNJõUJS M 2r k·q VL = - r k·q VK = - r olarak hesaplan›r. &MFLUSJLTFMQPUBOTJZFMTLBMFSCJSCÑZÑLMÑLPMEVôVOEBO, - WF . OPLUBMBSOO FMFLUSJLTFM QPUBOTJZFMMFSJ BSBTOEB 7M >7K =7LJMJöLJTJWBSES + + +q + + O+ ÖRNEK 9 + + :ÐLMFSJWFZBS¿BQMBSTSBTJMF-R +RWFS SPMBO J¿JCPõJMFULFO9WF:LÐSFMFSJõFLJMEFLJHJCJJ¿J¿FZFS- ++ MFõUJSJMNJõUJS V kq qxmR r qyR O, L M r ÞE rrrrr öMFULFO LÐSFOJO EõOEB FMFLUSJLTFM QPUBOTJZFM #VOBHÌSF, -WF.OPLUBMBSOOFMFLUSJLTFMQPUBO- IFTBC ZBQBSLFO CÐUÐO ZÐL NFSLF[EF UPQMBO- TJZFMMFSJOJIFTBQMBZO[ Nõ OPLUBTBMZÐL HJCJIFTBQMBNBMBSZBQMBCJ- MJS 30 8. 7M7K7L

www.aydinyayinlari.com.tr &-&,53÷,4&-,677&5m\"-\"/105\"/4÷:&-%·;(·/&-&,53÷,\"-\"/7&4*ó\" 5. MODÜL 11. SINIF r, OPLUBTOOFMFLUSJLTFMQPUBOTJZFMJOJIFTBQMBZBSBLCBö- ²ODFMJLMF,WF-OPLUBMBSOOFMFLUSJLTFMQPUBOTJZFMMFSJ- OJIFTBQMBZBMN MBZBMN,OPLUBTIFSJLJJMFULFOLÑSFOJOEFJÀJOEFPMEV- ôVOEBOCVOPLUBOOFMFLUSJLTFMQPUBOTJZFMJIFTBQMBOS- LFO k·q CBôOUTOEBEZFSJOFLÑSFMFSJOZBSÀBQMB- #VOBHÌSF d k·qx k·qy 2r 3r SZB[MS VK = + #VOBHÌSFCVOPLUBOOFMFLUSJLTFMQPUBOTJZFMJ V = k·qx + k·qy k·3q k (- 2q) kq 4r 4r L VK = 2r + 4r = r PMBSBLIFTBQMBOS PMBSBLCVMVOVS r- OPLUBTOO FMFLUSJLTFM QPUBOTJZFMJ IFTBQMBOSLFO - VK = 2 JTF7KWF7LZFSJOFZB[MSTB OPLUBT 9 JMFULFO LÑSFTJOJO JÀJOEF PMEVôVOEBO CV LÑ- VL 3 SFOJO CV OPLUBEB PMVöUVSEVôV FMFLUSJLTFM QPUBOTJZFM IF- TBQMBOSLFO E ZFSJOF CV LÑSFOJO ZBSÀBQ BMOSLFO - k·q + k·qy OPLUBT : JMFULFO LÑSFTJOJO EöOEB PMEVôVOEBO CV LÑ- SFOJO CV OPLUBEB PMVöUVSEVôV FMFLUSJLTFM QPUBOTJZFM IF- x TBQMBOSLFO E ZFSJOF LÑSFOJO NFSLF[JOJOEFO CV OPLUB- ZBPMBOV[BLMLBMOS#VOBHÌSFCVOPLUBOOFMFLUSJLTFM 2r 3r = 2 JGBEFTJOF VMBöMS (FSFLMJ JöMFNMFS QPUBOTJZFMJ 3 ZBQMEôOEB k·qx k·q + y 4r 4r qX =- 1 PMBSBLCVMVOVS q 2 Y k·(- 2q) k·3q kq VL = += 4r 3r 2r ÖRNEK 11 PMBSBLIFTBQMBOS :ÐLMFSJWFZBS¿BQMBSTSBTJMF+R -RWFS SPMBO J¿MFSJ CPõ JMFULFO , WF - LÐSFMFSJ õFLJMEFLJ HJCJ J¿ J¿F r.OPLUBTOOFMFLUSJLTFMQPUBOTJZFMJIFTBQMBOSLFOEZF- ZFSMFõUJSJMNJõUJS SJOF CV OPLUB JLJ JMFULFO LÑSFOJO EF EöOEB PMEVôVOEBO CVOPLUBOOLÑSFMFSJONFSLF[MFSJOEFOPMBOV[BLMLMBSZB- L –q [MBSBLIFTBQMBOS#VOBHÌSFCVOPLUBOOFMFLUSJLTFMQP- UBOTJZFMJ , +2q k·3q k·(- 2q) kq OA VM = 5r + = r r r r r r qA 5r 5r PMBSBLIFTBQMBOS ÖRNEK 10 \"OPLUBTOEBTBCJUUVUVMBOR\"ZÑLÑOÑOFMFLUSJLTFM kq2 :ÐLMFSJWFZBS¿BQMBSTSBTJMFRx RyWFS SPMBOJMFU- LFOJ¿MFSJCPõ9WF:LÐSFMFSJõFLJMEFLJHJCJJ¿J¿FZFS- QPUBOTJZFMFOFSKJTJ- 2r JTFR\"ZÑLÑLBÀREVS MFõUJSJMNJõUJS \"OPLUBTOOFMFLUSJLTFMQPUBOTJZFMJ Y qy X qx EPA = k · 2q· q A + k (- q)·qA = k·q·qA 6r 6r 6r O , L CBôOUTJMFIFTBQMBOS r rr r k·q2 EPA = - 2r ,WF-OPLUBMBSOOFMFLUSJLTFMQPUBOTJZFMMFSJPSBO JTFCVJLJCBôOUCJSCJSJOFFöJUMFOEJôJOEFR\"ZÑLÑ k·q·qA = - k·q2 2 JTFLÑSFMFSJOZÑLMFSJPSBO qx LBÀUS 6r 2r 3 qy JGBEFTJOEFO R\" = -R PMBSBLCVMVOVS kq kq kq 31 10. - 1 9. VK = r VL = 2r VM = 5r 2 11. mR

TEST - 1 &-&,53÷,4&-105\"/4÷:&-&/&3+÷7&&-&,53÷,4&-105\"/4÷:&- 1. \"öBôEBLJJGBEFMFSEFOIBOHJTJZBOMöUS 4. O \"ZO EÐ[MFNEF CVMVO BO \" &MFLUSJLTFMQPUBOTJZFMTLBMFSCJSCÐZÐLMÐLUÐS 2a 2a +R RxWF+q yüklerinin a LPOVNMBSõFLJME FLJHJCJEJS # )FSIBOHJ CJS OPLUBOO FMFLUSJLTFM QPUBOTJZFMJ +$MJL CJSJN ZÐLÐO TPOTV[EBO P OPLUBZB UB- +q qX +q õONBTTSBTOEBZBQMBOJõFFõJUUJS :ÑLMFSJO 0 OPLUBT OEB PMVöUVSEVLMBS CJMFöLF $ &MFLUSPOMBS QPUBOTJZFMJ LÐ¿ÐL CJS OPLUBEBO QP- FMFLUSJLTFMQPUBOTJZFMTGSPMEVôVOBHÌSFR9ZÑ- UBOTJZFMJCÐZÐLCJSOPLUBZBEPóSVIBSFLFUFEFS LÑLBÀREVS % öMFULFO CJS LÐSFOJO J¿JOEFLJ IFS OPLUBEBLJ FMFLU- \" - 1 # - 1 $ % 1 & m SJLTFMQPUBOTJZFMMFSCJSCJSJOFFõJUUJS 4 2 2 & :ÐLMÐ JLJ LÐSF JMFULFO CJS UFM JMF CJSMFõUJSJMJSTF JLJ LÐSFBSBTOEBNVUMBLBZÐLHF¿JõJPMVS 2. -2WF+2ZÐLMFSJõFLJMEFLJHJCJ\"WF#OPL- 5. R E +q UBMBSOBTBCJUMFONJõUJS +R +R -R WF -2q m2 , LMN 2 ZÐLMFSJ õFLJMEFLJ HJCJ CJS A E EE B O LBSFOJO LËõFMFSJOF TBCJU- E E E E MFONJõMFSEJS /PLUBMBS BSBT V[BLMLMBS FöJU PMEVôVOB HÌSF - –2q E –2q OPLUBTOOQPUBOTJZFMJ7LOFEJS ]\",]],-]]-.]]./]]/#]E \" -kQ # +kQ $ -2kQ ,FOBSV[VOMVôVEPMBOLBSFOJOLÌöFMFSJOFZFS- 3d 3d 3d MFöUJSJMFOZÑLMFSJO0OPLUBTOEBPMVöUVSBDBLMB- SFMFLUSJLTFMQPUBOTJZFMJOFPMVS % +kQ & 4GS 4d \" k q # 2 kq $ - 4 kq d d d % kq & 4GS 2d 3. ôFLJMEFLJLFOBSV[VOMVLMBSEWFEPMBOEJL- 6. +q a +q EËSUHFOJO\"WF#LËõFMFSJOFTSBTJMFRAWF-2 +R +RWF-RZÐLMFSJFõ- ZÐLMFSJTBCJUMFONJõUJS qA E LFOBS Ð¿HFOJO LËõFMFSJ- A a a OF õFLJMEFLJ HJCJ ZFSMFõUJ- SJMNJõUJS E –q B C &öLFOBS ÑÀHFOJO LÌöFMFSJOEFLJ ZÑLMFSJO PMVö- m2 UVSEVôV TJTUFNJO FMFLUSJLTFM QPUBOTJZFM FOFSKJ- TJBöBôEBLJMFSEFOIBOHJTJOFFöJUUJS %JLEÌSUHFOJO$OPLUBTOEBLJFMFLUSJLTFMQPUBOTJ- \" -kq2 # kq2 $ 2kq2 ZFMTGSJTF\"OPLUBTOEBLJR\"ZÑLÑLBÀ2EVS a a a \" # m $ % & % -3q2 & 3kq2 a a 1. E 2. B 3. \" 32 4. E 5. E 6. \"

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TEST - 3 &-&,53÷,4&-105\"/4÷:&-'\"3,*7&&-&,53÷,4&-÷õ 1. :ÐLÐ Y-$ PMBO OPLUBTBM QBS¿BDó CJS \" 4. :ÐLMFSJWFZBS¿BQMBSTSBTJMF+RWF-R SWF OPLUBTOEBO#OPLUBTOBHËUÐSNFLJ¿JOZBQMBOJõ SPMBOJMFULFO,WF-LBCVLMBSõFLJMEFLJHJCJJ¿ +EJS J¿FZFSMFõUJSJMNJõMFSEJS #VOBHÌSFCVJLJOPLUBOOFMFLUSJLTFMQPUBOTJ- L –3q ZFMGBSLLBÀ7EJS \" Y # Y $ Y K +q % Y & Y O B A r rr r –q #VOB HÌSF \" OPLUBTOEBLJ -R ZÑLÑOÑ \" OPLUBTOEBO#OPLUBTOBUBöNBLJÀJOZBQMBO FMFLUSJLTFMJöLBÀ k·q2 EJS 2. :ÑLMÑ CJS UBOFDJôJO FUSBGOEBLJ Fö QPUBOTJZFM d ZÑ[FZMFSMFJMHJMJPMBSBLBöBôEBWFSJMFOJGBEFMFS- \" # $ % & EFOIBOHJMFSJEPôSVEVS * &MFLUSJLTFM QPUBOTJZFMMFSJ FõJU PMBO OPLUBMBSO PMVõUVSEVóVZÐ[FZMFSEJS ** &õQPUBOTJZFMZÐ[FZMFSJMFFMFLUSJLBMBO¿J[HJMFSJ EBJNBCJSCJSJOFEJLUJS *** #JSFõQPUBOTJZFMZÐ[FZÐ[FSJOEFCJSFMFLUSJLZÐ- LÐOÐIBSFLFUFUUJSEJóJNJ[EFJõZBQMNB[ \" :BMO[* # *WF** $ *WF*** % **WF*** & * **WF*** 5. /PLUBTBM+RZÐLÐOÐOFUSBGOEBFõJUBSBMLMBSMBFõ QPUBOTJZFM ZÐ[FZMFSJ õFLJMEF WFSJMNJõUJS +q yükü- OÐO-OPLUBTOEBPMVõUVSEVóVFMFLUSJLTFMQPUBOTJ- ZFM7EJS 3. \"WF#OPLUBMBS+RZÐLÐOEFOTSBTJMFEWF +q L EV[BLMLUBES K A 3d M 2d #VOBHÌSF,WF.OPLUBMBSBSBTFMFLUSJLTFM QPUBOTJZFMGBSLLBÀ7EJS +q B \" # $ % & 12 +RZÐLÐOÐO#OPLUBTOEBPMVõUVSEVóVFMFLUSJLTFM QPUBOTJZFM7EJS #VOBHÌSF\"WF#OPLUBMBSBSBTFMFLUSJLTFM QPUBOTJZFMGBSLLBÀ7EJS \" # $ % & 1 2 1. \" 2. E 3. D 38 4. E 5. $

&-&,53÷,4&-105\"/4÷:&-'\"3,*7&&-&,53÷,4&-÷õ TEST - 4 1. +RZÐLMÐCJSDJTJNõFLJMEFHËTUFSJMFO0OPLUBTOB 3. ôFLJMEFLJLFOBSV[VOMVóVBPMBOEÐ[HÐOBMUHFOJO TBCJUMFONJõUJS LËõFMFSJOF-R +RWF-RZÐLMFSJLPOVMNVõUVS O K L MN –6q +q d +q d d d a ,OPLUBTOEBLJ+RZÐLMÐQBS¿BDLTFSCFTUCSBLM- a +2q EóOEB-OPLUBTOEBOjI[ZMBHF¿JZPS a a A a a #VOBHÌSF,OPLUBTOEBOTFSCFTUCSBLMBO+R –q B ZÑLMÑ QBSÀBDL / OPLUBTOEBO LBÀ j I[ZMB HFÀFS \" 2 2 # 3 $ 1 :ÐLMFSJO\"WF#OPLUBMBSOEBPMVõUVSEVóVFMFLU- 3 2 2 SJLTFMQPUBOTJZFMMFSTSBTZMB7AWF7BEJS % 3 & 8 #VOBHÌSF\"WF#OPLUBMBSOOFMFLUSJLTFMQP- 3 3 k·q UBOTJZFMGBSL 7\"# LBÀ a ES \" # $ % & 1 2. \"öBôEB WFSJMFO TJTUFNMFSEFO IBOHJMFSJOEF LF- 4. +RWF-RZÐLMÐJMFULFOMFWIBMBSõFLJMEFLJHJCJLBS- TJLMJ ÀJ[HJMFSMF CFMJSUJMFO FôSJMFS Fö QPUBOTJZFM õMLMUVUVMNBLUBES FôSJMFSJEFôJMEJS +q –q A) E B) L r K +q N M C) D) ,OPLUBTOEBLJ+RZÑLMÑDJTNJ,OPLUBTO- rq EBO-OPLUBTOBUBöNBLJÀJOZBQMBOJö81 , ,EFO.ZFUBöNBLJÀJOZBQMBOJö82 ,EFO q /ZFUBöNBLJÀJOZBQMBOJö83JTF81 , W2 WF83ÑOEPôSVCÑZÑLMÑLLBSöMBöUSNBTBöB- E) ôEBLJMFSEFOIBOHJTJEJS +q + + \" 83 >81 =82 # 81 =82 =83 + + $ 83 >81 >82 % 81 =82 >83 + + + & 82 >81 >83 1. B 2. D 39 3. $ 4. \"

TEST - 5 &-&,53÷,4&-105\"/4÷:&-'\"3,*7&&-&,53÷,4&-÷õ 1. %Ð[HÐO CJS FMFLUSJL BMBO BõBóEBLJ HJCJ PMVõUVSVM- 3. &MFLUSJLTFM Jö JMF JMHJMJ BöBôEB WFSJMFO JGBEFMFS- NVõUVS EFOIBOHJTJZBOMöUS E MN \" &MFLUSJLTFMLVWWFUMFSJOZBQUóJõOFHBUJGUJS L # &MFLUSJLTFMLVWWFUMFSFLBSõZBQMBOJõQP[JUJGUJS K $ \"ZO Fõ QPUBOTJZFM ZÐ[FZ Ð[FSJOEF CJS ZÐLÐ IB- #VOBHÌSF+RZÑLMÑCJSQBSÀBDLJÀJO SFLFUFUUJSEJóJNJ[EFFMFLUSJLTFMJõZBQMNB[ * ,OPLUBTOEBO-OPLUBTOBHËUÐSÐMÐSTFFMFLU- % &MFLUSJLTFM LVWWFUMFSF LBSõ Jõ ZBQMEóOEB TJT- SJLTFMJõZBQMNB[ UFNJOFMFLUSJLTFMQPUBOTJZFMFOFSKJTJBSUBS ** .OPLUBTOEBO-OPLUBTOBHËUÐSÐMÐSTFFMFLU- & 1P[JUJGZÐLMÐJMFULFOCJSLBCVóVOJ¿JOEFLJCJSZÐL SJLTFMLVWWFUMFSFLBSõJõZBQMS JMFULFO J¿FSJTJOEF IBSFLFU FUUJSJMJSLFO FMFLUSJLTFM JõZBQMS *** /OPLUBTOEBO.OPLUBTOBUBõOEóOEB FMFLUSJLTFMJõZBQMNB[ ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[* # *WF** $ *WF*** % **WF*** & * **WF*** 2. +R WF -R ZÐLMÐ QBS¿BDLMBS õFLJMEFLJ LPOVNEB 4. #JSEJLÐ¿HFOJOLËõFMFSJOEFOCJSJOF+RZÐLMÐQBS- TBCJUMFONJõUJS ¿BDLõFLJMEFLJHJCJTBCJUMFONJõUJS +q –q K d 53° #VZÑLMFSFUSBGOEBPMVöBOFöQPUBOTJZFMZÑ[FZ- L MFSJÀJ[JOJ[ A) B) +q +q +q –q +RZÑLÑOÑO,OPLUBTOEBPMVöUVSEVôVFMFLU- –q SJLTFM QPUBOTJZFM 7 JTF -3 n$ ZÑLÑ , OPLUBTOEBO-OPLUBTOBUBöNBLJÀJOZBQMBO FMFLUSJLTFMJöLBÀ+EÑS n$=-6$ C) D) \" -Y-6 # -Y-6 +q –q +q –q $ Y-6 % Y-6 E) –q & Y-6 +q 1. D 2. \" 40 3. E 4. B

&-&,53÷,4&-105\"/4÷:&- KARMA TEST - 1 1. qA qB ôFLJMEFLJ EJLEËSU- 4. A 12μc öLJ[LFOBSÐ¿HFOJOLËõF- B HFOJO \" LËõFTJOF lerine 12 n$ - 3 n$WF A -2 n$MVL # B 3 n$ZÐLMFSJõFLJMEFLJHJ- LËõFTJOF p-2 –3μc CJTBCJUMFONJõUJS 6m n$MVLZÐLMFSLPOV- O C D 3μc C ZPS 8m #VOBHÌSF $WF%OPLUBMBSOOFMFLUSJLTFMQP- #VOBHÌSFJLJ[LFOBSÑÀHFOJO\" # $LÌöFMF- UBOTJZFMGBSL 7$% LBÀWPMUUVS SJOEFLJ ZÑLMFSJO 0 OPLUBTOEB PMVöUVSEVLMBS f k = 9.109 N·m2 , 1nC = 10–6C p FMFLUSJLTFMQPUBOTJZFMJLBÀWPMUUVS C2 ]AO ]p]BO ]DN Lp9 N.m2 C2 1n$m$ \" # $ % & 36 \" Y # Y $ Y % Y & Y 2. qy qxWFRy yükü ile yük- MÐ0NFSLF[MJ J¿MFSJCPõ Y L JMFULFO9WF:LÐSFMF- X qx K 5. 2μc +2 n$MVL ZÐL õFLJMEFLJ O A HJCJTBCJUMFONJõUJS r r r r SJõFLJMEFLJHJCJEJS R ZÑLMÑ CJS DJTNJ -EFO ,ZF UBöNBL JÀJO 3m ZBQMBOJöTGSPMEVôVOBHÌSF * ,ÐSFMFSOFHBUJGZÐLMFZÐLMÐEÐS #VOBHÌSFn$MVLCJSZÑLÑONFUSFV[BôO- ** :OJOZÐLNJLUBS 9JOZÐLNJLUBSOEBOGB[MBES EBLJ \" OPLUBTOEB NFZEBOB HFUJSEJôJ FMFLUSJL- *** , WF - OPLUBMBSOO FMFLUSJLTFM QPUBOTJZFMMFSJ TFMQPUBOTJZFMLBÀWPMUUVS CJSCJSJOFFõJUUJS L=p9 N·m2 ; 1n$=-6 $ C2 ZBSHMBSOEBOIBOHJMFSJLFTJOMJLMFEPôSVEVS \" # $ % & \" :BMO[* # *WF** $ *WF*** % **WF*** & * **WF*** 6. q = 2·10–14C .OPLUBTOEBLJ 2=p-12 $MVL 3. + + ôFLJMEFLJZÐLÐp-$ K ZÐLõFLJMEFLJCJS PMBO NFUSF ZBS¿BQM 3m EJLÐ¿HFOJOLËõF- ++ LÐSF NFUSFZBS¿BQM TJOFTBCJUMFONJõUJS ZÐLTÐ[ LÐSFZF EPLVOEV- L 4m + + SVMVZPSWFV[BLMBõUSMZPS M ++ + Q = 6·10–12C r1 = 0,1 m r2 = 0,3 m #VOB HÌSF , OPLUBTOEBLJ R = 2 · 10-14 $MVL ZÑLÑ-ZFUBöNBLJÀJOLBÀ+MJLJöZBQMNBMES #VOB HÌSF CÑZÑL LÑSFOJO ZÑ[FZJOJO FMFLUSJLTFM Lp9 N·m2 QPUBOTJZFMJLBÀWPMUPMVS C2 f k = 9·109 N·m2 p \" Y- # Y- $ Y- C2 \" # $ % & % Y- & Y- 1. E 2. E 3. B 41 4. D 5. \" 6. $

KARMA TEST - 2 &-&,53÷,4&-105\"/4÷:&- 1. q1 = –q d q1 R2WFR3 yük- 3. +R -RWF+RZÐLMÐLÐSFMFSõFLJMEFLJHJCJTB- MFSJ õFLJMEFLJ BMUHF- d d OJOLËõFMFSJOFTBCJU- CJUMFONJõUJS +q O –3q 20 cm 20 cm O q2 MFONJõUJS %Ð[HÐO BMUHFOJO 20 cm d d d LËõFMFSJOEFLJ R1 +3q q3 q2WFR3 yüklerinin 0 OPLUBTOEB PMVõ- UVSEVLMBSCJMFõLFFMFLUSJLBMBOTGSES #V ZÑLMÑ LÑSFMFSJO 0 OPLUBTOEB NFZEBOB HF- UJSEJôJ UPQMBN FMFLUSJLTFM QPUBOTJZFM WPMU #VOBHÌSF0OPLUBTOEBLJUPQMBNFMFLUSJLTFM PMEVôVOBHÌSFRZÑLÑLBÀ$EVS n$m$ L9 Nm2$2 QPUBOTJZFMJLBÀUS L=$PVMPNCTBCJUJ k·q 2k·q 3k·q \" - # $ - d 4k·q d k·q d \" Y- # Y- $ Y- & % d % Y- & Y- d 2. ôFLJMEFLJ,OPLUBTOEBLJRxZÐLÐTBCJUUVUVMVQ. 4. q1 R2 R3WFRZÐLMFSJõFLJMEFLJLBSFOJOLËõF- MFSJOFTBCJUMFONJõUJS OPLUBTOEBLJRyZÐLÐIBSFLFUMJEJS q1 = –2q q2 = +2q qx qy O KLM q4 = +q q3 = –2q #VEVSVNEB RyZÐLÐ.OPLUBTOEBO-OPLUBTOB #VLBSFOJOLËõFMFSJOFLPOVMNVõZÐLMFSEFORÐO0 UBõONBLUBES#VQSPCMFNMFVóSBõBO%FGOFZBQMBO OPLUBTOEBLJFMFLUSJLTFMQPUBOTJZFMJ7EJS JõJO QP[JUJG PMEVóVOV IFTBQMZPS #V CJMHJMFSMF ±[- MFNEFOZPSVNMBSZBQNBTOJTUJZPS #VOB HÌSF EÌSU ZÑLÑO 0 OPLUBTOEBLJ UPQMBN FMFLUSJLTFMQPUBOTJZFMJOFEJS *öLJDJTJNBZODJOTZÐLMFZÐLMÐEÐS \" 7 # -7 $ V % - V & 7 22 ²[MFN **öLJDJTJN[UDJOTZÐLMFZÐLMÐEÐS 5. &MFLUSJLTFMQPUBOTJZFMLPOVTVOEB ËóSFUNFOBõBóEB- LJõFLJMEFWFSJMFO, -WF.OPLUBMBSOOFMFLUSJLTFMQP- UBOTJZFMMFSJOJËóSFODJMFSJOJOLBSõMBõUSNBTOJTUJZPS ²[MFN +12q KLM –60q d dd d ***#VEVSVNEBFMFLUSJLTFMLVWWFU- , -WF.OPLUBMBSOOQPUBOTJZFMMFSJTSBTJMF7, MFSJõZBQNõUS 7-WF7MEJS ²[MFN #VOBHÌSF7K 7LWF7MQPUBOTJZFMMFSJJÀJO EPôSVLBSöMBöUSNBBöBôEBLJMFSEFOIBOHJTJEJS #VOBHÌSF²[MFNJOZBQUôZPSVNMBSEBOIBOHJ- MFSJEPôSVEVS \" 7, =7- =7M # 7M >7- >7, \" :BMO[* # :BMO[** $ :BMO[*** $ 7, >7M >7- % 7, >7- >7M % *WF** & *WF*** & 7- >7, >7M 1. $ 2. \" 42 3. E 4. B 5. D

&-&,53÷,4&-105\"/4÷:&- KARMA TEST - 3 1. %Ð[HÐOCJSFMFLUSJLBMBOJ¿JOEFLJ+RZÐLÐGBSLMZPM- 3. +2 n$MVLZÐLõFLJMEFLJHJCJTBCJUMFONJõUJS MBSMB,OPLUBTOEBO/OPLUBTOBUBõONBLJTUFOJ- 2μc ZPS A M r 3m 4 · 10m $MVL CJS ZÑLÑ TPOTV[EBO \" OPLUBTOB HFUJSNFLJÀJOLBÀKPVMFMÑLJöZBQMNBMES K rL rN N·m2 C2 ôFLJMEFLJ , WF / OPLUBMBSOO FMFLUSJLTFM QPUBO- Lp9 n$m$ TJZFMMFSJ GBSLMES R ZÐLÐOÐO ,.-/ ,-/ WF ,./ ZPMMBS CPZVODB IBSFLFUJ TSBTOEB ZBQMBO \" # m $ % & m FMFLUSJLT FMJõMFSTSBTZMB81 82 83 UÐS #VJöMFSBSBTOEBLJCÑZÑLMÑLJMJöLJTJOBTMES \" 81 =82 =83 # 81 =82 <83 4. \"ZODJOTZÐLMÐJ¿MFSJCPõ,WF-LÐSFMFSJOJOZÐ- $ 81 <82 =83 % 81 =83 <82 [FZMFSJOEFLJ FMFLUSJL BMBOMBSOO CÐZÐLMÐóÐ FõJUUJS Bu durumda kürelerin yüzeylerindeki elektriksel & 82 <83 <81 QPUBOTJZFMMFSTSBTJMF7,WF7-EJS K 2r L r 2. ôFLJMEFLJ JMFULFO MFWIBMBS CJSCJSJOF QBSBMFM PMVQ [U #VOB HÌSF LÑSFMFSJO ZÑ[FZMFSJOEFLJ FMFLUSJLTFM QPUBOTJZFMMFSJOPSBO VK LBÀUS DJOTZÐLMFZÐLMÐEÐS VL ++++++ B 12 3 \" # $ % 1 & 1 4 24 A –––––– RZÐLMÐCJSQBS¿BDL\"OPLUBTOEBO#OPLUBTOB 5. +2ZÐLÐõFLJMEFLJHJCJTBCJUMFONJõUJS WFZPMMBSJ[MFOFSFLUBõOEóOEBZBQMB- d DBLJõMFSTSBTJMF81 82 83WF8UÐS +Q K L #VOBHÌSF81 , W2 , W3WF84BSBTOEBOBTM CJSJMJöLJWBSES \" 81 >82 >83 >8 &MFLUSJLTFMQPUBOTJZFMMFSJTSBTZMB7,WF7-PMBO # 81 =8 >82 >83 ,WF-OPLUBMBSBSBTOEBLJV[BLMLELBEBSES $ 83 >82 >81 =8 % 83 >82 >81 >8 #JSRZÑLÑOÑO,EFO-ZFHÌUÑSÑMNFTJTSB & 81 =82 =83 =8 TOEBZBQMBOFMFLUSJLTFMJöJOCVMVOBCJMNFTJJÀJO BöBôEBLJ OJDFMJLMFSEFO IBOHJMFSJOJO CJMJONFTJ HFSFLMJEJS \" RWFE # 7,WFE & 2WF7, % 7-WFE & R 7,WF7- 1. \" 2. E 43 3. $ 4. B 5. E

KARMA TEST - 4 &-&,53÷,4&-105\"/4÷:&- 1. ôFLJMEFLJ EJLEËSUHFOJO LËõFTJOEFLJ . OPLUBTO- 3. ôFLJMEFLJ,WF-OPLUBMBSOOFMFLUSJLTFMQPUBOTJ- daki +RZÐLÐTBCJUUVUVMVZPS ZFMMFSJCJSCJSJOEFOGBSLMES,OPLUBTOEBLJ+q yü- LÐ-OPLUBTOBUBõONBLJTUFOJZPS +20q L M 2 KL q 1 3d N 4d K sonsuza 34 gider sonsuzdan gelir #VöFLJMÑ[FSJOEF+RZÑLÑOÑ,OPLUBT OEBO #VOBHÌSFöFLJMEFLJIBOHJZPMJ[MFOJSTFZBQMBO - OPLUBTOB HÌUÑSNFLMF FMFLUSJLTFM LVWWFUMFSF FMFLUSJLTFMJöFOGB[MBPMVS LBSöOFLBEBSJöZBQMS kq2 # kq2 $ kq2 \" # d2 d 2d \" $ % % 2kq2 & kq2 & #ÐUÐOZPMMBSJ¿JOFMFLUSJLTFMJõBZOES 3d 3d 2. q1 R2WFR3ZÐLMFSJõFLJMEFLJLPOVNMBSOEBTBCJU 4. ôFLJMEFLJTJTUFNEF+RWF-RZÐLMFSJCFMJSUJMFOLP- UVUVMNBLUBES OVNMBSEBTBCJUUJS q1 = +q KLM dddd 0 +q –q q3 ,OPLUBTOEBOTFSCFTUCSBLMBO+RZÑLMÑDJTJN q2 = +2q Ñ[FSJOFZBQMBOFMFLUSJLTFMJöMFSMFJMHJMJPMBSBL \"ZOEÐ[MFNJ¿JOEFLJR1 = +R R2 = +RWFR3 * ,EFO-ZFHFMJSLFOFMFLUSJLTFMLVWWFUMFSJõ yükMFSJOJO 0 OPLUBTOEB PMVõUVSEVóV FMFLUSJLTFM ZBQNõUS QPUBOT JZFMTGSES ** -EFO.ZFHFMJSLFOFMFLUSJLTFMLVWWFUMFSFLBS- #VOBHÌSFR3ZÑLÑLBÀREVS õJõZBQMNõUS #JSJNLBSFMFSË[EFõUJS *** ,EFO-ZFHFMJSLFOZBQMBOJõ -EFO.ZFHF- MJSLFOZBQMBOJõFFõJUUJS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" -R # -R $ - 3q \" :BMO[* # :BMO[** $ *WF** & + q % -R % *WF*** & **WF*** 1. B 2. D 44 3. E 4. D

&-&,53÷,4&-105\"/4÷:&- KARMA TEST - 5 1. ôFLJMEFLJ, - .OPLUBMBS ZBMO[+q yükünün 4. :BS¿BQMBSWFZÐLMFSJõFLJMEFHËTUFSJMFO, - . PMVõUVSEVóVFMFLUSJLBMBOJ¿JOEFCVMVONBLUBES LÐSFMFSJJMFULFOUFMMFSMFCJSCJSJOFCBóMBOZPS O KLM +QK +QL 3r 2r +QM +q r K m- WF -m. OPLUBMBS BSBTOEBLJ FMFLUSJLTFM QPUBOTJZFMGBSLMBSOPSBO VKL LBÀUS K LM ]0,] = ],-] = ]-.] VLM ,ÑSFMFSBSBTZÑLHFÀJöJEVSEVôVOEB \" 1 # $ 3 % & * 2,2-2M 2 2 ** 2,2-2M *** 7,7-7M JGBE FMFSJOEFOIBOHJMFSJEPôSVPMVS \" :BMO[* # :BMO[** $ :BMO[*** 2. #JSEJLEËSUHFOJOLËõFMFSJOFZFSMFõUJSJMFO+RWF+2q % *WF*** & **WF*** OPLUBTBMZÐLMFSJOJOLPOVNMBSõFLJMEFLJHJCJEJS 2d +2q KL dd 5. +RZÐLÐõFLJMEFLJLPOVNEBTBCJUMFONJõUJS L K j0 L +q +q –q ,OPLUBTOOQPUBOTJZFMJWPMUPMEVôVOBHÌ- õFLJMEFLJ TÑSUÑONFTJ[ TJTUFNEF - OPLUBTO- SF+$MVLCJSZÑLÑ,EFO-ZFHÌUÑSNFLJÀJO EBO j0 JML I[ JMF BUMBO -R ZÑLÑ , OPLUB- ZBQMBOFMFLUSJLTFMJöLBÀKPVMFEÑS TOEBO HFÀFSLFO BöBôEBLJMFSEFO IBOHJTJ EPô- SVPMVS \" # $ % & \" -RZÐLÐOÐOLJOFUJLFOFSKJTJB[BMNõUS 3. –q +q -RWF+RZÐLMFSJõFLJMEFLJLP- # -RZÐLÐOÐOQPUBOTJZFMFOFSKJTJBSUNõUS OVNMBSBTBCJUMFONJõUJS $ -RZÐLÐOÐOQPUBOTJZFMFOFSKJTJB[BMNõUS % 4JTUFNJOQPUBOTJZFMFOFSKJTJBSUNõUS y -RWF+RZÐLMFSJOJOYWFZ & 4JTUFNJOLJOFUJLFOFSKJTJEFóJõNFNJõUJS OPLUBMBSOEBPMVõUVSEVLMBSCJMFõ- 6. \"öBôEBLJMFSEFO IBOHJTJ FMFLUSJLTFM QPUBOTJZFM x LF FMFLUSJL BMBO õJEEFUMFSJ TSB- TZMB &x WF &y CV OPLUBMBSO GBSLOCJSJNJPMBOWPMUBFöJUUJS FMFLUSJLTFMQPUBOTJZFMMFSJJTF7xWF7y ES #VOBHÌSF&x , EZWF7x 7ZBSBTOEBLJCÑZÑL- MÑLJMJöLJTJBöBôEBLJMFSEFOIBOHJTJHJCJEJS \" &x > Ey 7x >7y # &y > Ex 7y >7x \" joule # joule $ +PVMFYDPVMPNC $ &x = Ey 7x =7y % &x = Ey 7y >7x metre coulomb & &y > Ex 7x =7y % newton & coulomb coulomb metre 1. E 2. \" 3. E 45 4. E 5. $ 6. B

YAZILI SORULARI &-&,53÷,4&-105\"/4÷:&- 1. Yükleri -RWF+RPMBOFMFLUSJLZÐLMFSJõFLJMEFLJ 3. +R ZÐLÐOÐO FUSBGOEBLJ Fõ QPUBOTJZFM ZÐ[FZMFSJ LPOVNMBSEBTBCJUMFONJõMFSEJS BõBóEBLJõFLJMEFLJHJCJEJS –3q +q K L C +q A 2d B d d A BD #VOBHÌSF B CVZÐLMFSJO,WF-OPLUBMBSOEBPMVõUVSEVLMBS #VOBHÌSF B b ir +RZÐLÐIBOHJOPLUBMBSÐ[FSJOEFIBSFLFUFU- FMFLUSJLTFMQPUBOTJZFMMFSJIFTBQMBZO[ C, WF-OPLUBMBSBSBTFMFLUSJLTFMQPUBOTJZFM UJSJMJSTFFMFLUSJLTFMJõZBQMNB[ Cb ir +RZÐLÐIBOHJOPLUBMBSÐ[FSJOEFIBSFLFUFU- GBSLOFEJS UJSJMEJóJOEFFOGB[MBFMFLUSJLTFMJõZBQMS a. VK = k (- 3q) kq + =0 B#WF$OPLUBMBSOOFMFLUSJLTFMQPUBOTJZFMMFSJFöJUPMEV- 3d d ôVOEBO+RZÑLÑCVOPLUBMBSÑ[FSJOEFIBSFLFUFUUJSJMJSTF FMFLUSJLTFMJöZBQMNB[ = k (- 3q) kq kq V + =- C\"WF%OPLUBMBSBSBTFMFLUSJLTFMQPUBOTJZFMGBSLÀPLCÑ- 4d 2d 4d ZÑLUÑS#VZÑ[EFO+RZÑLÑCVOPLUBMBSÑ[FSJOEFIBSFLFU L FUUJSJMJSTFFOGB[MBFMFLUSJLTFMJöZBQMS C7KL =7L -7KCBôOUTJMFIFTBQMBOS#VOBHÌSF kq kq PMBSBLIFTBQMBOS V = - -0=- 4d 4d KL 2. :ÐLMFSJY-12$WF-Y-12$PMBOFMFLUSJL 4. ö¿JCPõSWFSZBS¿BQMJMFULFOLÐSFMFSJOZÐLMFSJ ZÐLMFSJEJLLFOBSV[VOMVLMBSNWFNPMBOEJL TSBTJMF+RWF-REVS Ð¿HFOJOLËõFMFSJOFõFLJMEFLJHJCJZFSMFõUJSJMNJõUJS +2q B qL = –2x10–12C –3q 4m OK L M rrrrr A qK = +12x10–12C 3m #VOBHÌSF#OPLUBTOEBLJRLZÑLÑOÑCVOPL- UBEBO\"OPLUBTOBUBöNBLJÀJOLBÀ+MJLJöZB- QMNBMES L=Y9 Nm2$2 W =RL7#\"CBôOUTJMFIFTBQMBOS #VOBHÌSF, -WF.OPLUBMBSOOFMFLUSJLTFM W =RL 7\" -7B JGBEFTJOEF QPUBOTJZFMMFSJOJIFTBQMBZO[ 7\"JMF7BEFôFSMFSJCVMVOVQZFSJOFZB[MSTB W = - 2x10-12 f 9x109 x12x10-12 - 9x109 x12x10-12 p k (- 3q) k·2q kq VK = 2r + 4r = - r 34 W = -18 x 10-15+PMBSBLCVMVOVS k (- 3q) k·2q kq VL = + =- 3r 4r 2r k (- 3q) k·2q kq VM = + =- 5r 5r 5r kq kq 2. mYm J 46 B B $ C\" D kq kq kq B7K 7Lm 4d Cm 4. VK = - r , VL = - 2r , VM = - 5r 4d

&-&,53÷,4&-105\"/4÷:&- YAZILI SORULARI 5. :ÐLMFSJ õFLJMEF WFSJMFO DJTJNMFS ôFLJM-IEFLJ LP- 7. Yükleri +R -RWFR,PMBODJTJNMFSLFOBSV[VO- OVNEBOôFLJM-IIEFLJLPOVNBHFUJSJMJZPS MBS õFLJMEF WFSJMFO Ð¿HFOJO LËõFMFSJOF ZFSMFõUJSJMJ- ZPS +3q +q dd –2q +3q +q d d 3d 2d –3q 4d qK –2q d +q ôFLJMmII #VTJTUFNJOUPQMBNFMFLUSJLTFMQPUBOTJZFMFOFS- KJTJTGSJTFRKZÑLÑLBÀREVS ôFLJMmI #VOB HÌSF TJTUFNJ õFLJM-IEFO õFLJM-IIEFLJ EPToplam = k·q·(- 3q) + k·q·qk + k·qk·(- 3q) =0 LPOVNBHFUJSNFLJÀJOZBQMBOFMFLUSJLTFMJöJIF- 3d 2d 4d TBQMBZO[ k·q·3q k·q (- 2q) k·3q (- 2q) - k·q2 = k·q·q k EP1 = d + d + d d 4d 5k · q 2 qK = - 4q'dur. =- d k (- 2q)·3q k·3q·q k·(- 2q)·q EP 2 = ++ d d 2d 4k · q 2 =- d W =Ô&1 = E1 - E1CBôOUTOEBOTJTUFNJõFLJM-IEFOõF- LJM-IIZFHFUJSNFLJÀJOZBQMBOFMFLUSJLTFMJö = - 4kq2 - f - 5kq2 p = kq2 PMBSBLCVMVOVS d dd 6. +q ôFLJMEFLJ EJL Ð¿HF- 8. -Y-16$MVLFMFLUSJLZÐLÐOÐTPOTV[EBO OJO LËõFMFSJOEFO CJ- SJOFZFSMFõUJSJMFO+ q +Y-16$ZÐLMÐDJTJNEFOELBEBSV[BLUBki bir OPLUBZBHFUJSNFLJ¿JOZBQMBOJõ- Y-23+EJS 4d ZÐLÐOÐO , OPLUB- 5d TOEB PMVõUVSEVóV FMFLUSJLTFM QPUBOTJ- +4x10–16 C A K 53° d L yel +WPMUUVS 3d #VOBHÌSFEV[BLMôOIFTBQMBZO[ –3x10–12 C L=Y9 Nm2$2 #VOB HÌSF - OPLUBTOEBLJ - 3 x 10-12$MVL FMFLUSJLZÑLÑOÑ,OPLUBTOBHÌUÑSNFLJÀJOZB- QMNBTHFSFLFOFMFLUSJLTFMJöJIFTBQMBZO[ L=Y9 Nm2$2 TJO= DPT= W =RÔ7=R 7TPO -7JML 7JML = 0 kq kq - 14, 4 x10-23 = - 2x10-16 f 9x109 x 4 x10-16 p VK = 4d = 20V ( = 80V'dir. d d d = 5m V = kq = 80 = 16V'dir. 5d 5 L W =R 7K -7L CBôOUTOEBO = - 3 x 10-12 - 20) = 12 x 10-12 J PMBSBLCVMVOVS kq 2 6. 12 x 10m J 47 7. mR 8. N 5. d

<(1m1(6m/6258/$5 &-&,53÷,4&-105\"/4÷:&- 1. 'J[JLEFSTJOEFFMFLUSJLTFMQPUBOTJZFMFOFSKJLBWSBN- 2. %FOJ[TFWJZFTJOEFOJUJCBSFOBZOZÐLTFLMJóFTBIJQ OËóSFOFO7FHB JõHÐ¿FOFSKJLPOVTVOEBËóSFOEJ- OPLUBMBSO CJSMFõUJSJMNFTJ JMF FMEF FEJMFO LBQBM Fõ óJ%ÐOZBZÐ[FZJOFZBLOCJSZFSEFOTFSCFTUCSBL- QPUBOTJZFM ZÐ[FZMFSJ DPóSBGZB CJMJNJOEF Fõ ZÐLTFM- MBOCJSDJTNJOLÐUMF¿FLJNQPUBOTJZFMFOFSKJTJOJOLJ- UJFóSJMFSJPMBSBLBEMBOESMS OFUJLFOFSKJZFEËOÐõUÐóÐHJCJFMFLUSJLTFMQPUBOTJZFM FOFSKJOJOEFLJOFUJLFOFSKJZFEËOÐõFCJMFDFóJCJSEF- OFZEÐ[FOFóJPMVõUVSNBLJTUJZPS m h jm #VOB HÌSF 7FHB JML IBSFLFU EVSVNV CBLNO- #FO[FSõFLJMEFFMFLUSJLBMBOEBFMFLUSJLTFMQPUBOTJ- EBOZVLBSEBLJFOFSKJEÌOÑöÑNÑJMFCFO[FSPMBO ZFMMFSJ FõJU PMBO OPLUBMBSO CJSMFõUJSJMNFTJ JMF PMVõBO BöBôEBWFSJMFOIBOHJEFOFZEÑ[FOFôJOJPMVöUV- ¿J[HJMFSFEFFõQPUBOTJZFM¿J[HJMFSJEFOJS SBCJMJS 4ÐSUÐONFMFSJINBMFEJMFDFLUJS #VOBHÌSFBöBôEBWFSJMFOÀJ[HJMFSEFOIBOHJMF- SJFMFLUSJLZÑLMFSJFUSBGOEBLJFöQPUBOTJZFMÀJ[- HJMFSJPMBCJMJS I. +q I. Nötr cisim Nötr cisim II. –q +q II. 2ZÐLMÐDJTJN 2ZÐLMÐDJTJN III. +q +q III. 2ZÐLMÐDJTJN m2ZÐLMÐDJTJN \" :BMO[* # *WF** $ **WF*** \" :BMO[* # :BMO[** $ :BMO[*** % *WF*** & * **WF*** % *WF** & **WF*** 1. $ 48 2. E

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TYT AYT 11. Sınıf Fizik Ders İşleyiş Modülleri Modül 5 Elektriksel Kuvvet ve Elektrik Alan Elektriksel Potansiyel Düzgün Elektrik Alan ve Sığa

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TYT AYT 11. Sınıf Fizik Ders İşleyiş Modülleri Modül 5 Elektriksel Kuvvet ve Elektrik Alan Elektriksel Potansiyel Düzgün Elektrik Alan ve Sığa

Description: TYT AYT 11. Sınıf Fizik Ders İşleyiş Modülleri Modül 5 Elektriksel Kuvvet ve Elektrik Alan Elektriksel Potansiyel Düzgün Elektrik Alan ve Sığa

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