CHAPTER III ELECTROSTATIC

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1 CHAPTER III ELECTROSTATIC Subject:. Electostatics inteaction and coulomb s law. Electic field 3. Gauss s law 4. Electic potential and electic potential enegy 5. Capacitos. Electostatics inteaction and coulomb the statement of coulomb s law the foce between two chaged object is diectly popotional to the coss poduct of thei chages and invesely popotional to the distance between them we can be expessed that statement by equation below: F= Coulomb foce (N) q = chage of object (C) q = chage of object (C) k= constant (9 x 0 9 ) mn C - = distance between q with q (m) k q F q whee k 4 o If the inteaction of electic chages occus in ai (vacuum) o = 8.85 x 0 - C N - m - But if inteaction of electic chage occus in anthe mateial mateial pemitivity elativetothevacuum mateial pemitivuty 0 ai vacuu pemitivity o change with whee o

2 Execise. Two chages each of 0 µc and 4 µc ae sepaated cm, calculate the epulsion foce on the chage if: a. both chages ae place in ai b. both chages ae place in a substance with = 5. at cone points of an equilateal tiangles ABC ae placed the chages each of q A = +0 µc, q B = -40 µc and q C = -40 µc, as shown in the following figue C A B If = 8 cm, detemine the foce that exets upon the chage q A 3. At the cone points of the squae ABCD ae placed the chages consecutively +q, -q, -q and q. the side length of the squae is s and the chage +q expeiences the foce of, detemine: a. medium whee the chages exist b. the value of n c. foce upon the chage of +q if q = 30 µc and s = 5 cm 4. at the cones of an equilateal tiangle that is cm in side length ae placed 3 chages, these ae q = 4 µc, q =3.4 µc and q 3 = -0 3 µc. Detemine the foce exets upon the chage q 3

3 5. an object that has mass of 0 gams and chage +0.5 µc. It is suspended on the sting as in the following figue T q=+ 0.5 µc q ' =- µc m=0 kg 5 cm If the sting mass is neglected calculate the sting tensional foce (T) 6. two changes each of 0 µc and -60 µc ae sepaated 8 cm. if the chages ae placed on the substance that has the elative pemittivity of 8, calculate the coulomb s foce on the chages 7. A paticle chaged + 5 µc is placed on a connecto line and between two chaged paticles of -9 µc and -4 µc that sepaated 0.5 m. detemine the position of paticle +5 µc so hat is not undego the coulomb s foce fom the two othe chages -9 µc +5 µc -4 µc 8. ada empat buah muatan A, B, C, D. A mmenaik B. A enolak C, dan C menaik D. Bila C bemuatan negatif tentukan jeis muatan-muatan lainnya 9. Hitunglah nilai pebandingan antaa gaya coulomb dengan gaya gavitasi yang dikejakan oleh sebuah poton tehadap poton lainnya 0. dua keping uang logam masing-masing dibei muatan sama, tepisah sejauh 5 cm. Gaya tolak menolak antaa 3

4 kedua uang logam 6,4 x 0-6 N. Hitunglah muatan masing-masing uang logam jika keduanya beada: a. di udaa b. di dala ai yang pemitifitas elatifnya 80. muatan titik A, 50 µc, diletakkan pada gais hubung antaa muatan titik B, 50 µc, dan muatan titik C, -300 µc. Muatan titik A diletakkan 5 cm dai B dan 0 cm dai C. Tentukan besa dn aah gaya yang bekeja pada muatan titik A. bola kecil A bemuatan +35 µc dan bola kecil B bemuatan -60 µc tepisah sejauh 0 cm. Bola kecil C yang bemuatan diletakkan pada gais hubung antaa A dan B sehingga esultan yang bekeja pada C sama dengan nol. Dimana letak C diuku dai A? 3. Muatan q = - x 0-6 Cdan q = 3 x 0-6 C teletak masing-asing pada titik A (8,0) dan B (0,0) dalam suatu sistim koodinat katesius. Semua satuan panjang dala sm. Hitungllah besa dan aah gaya pada muatan q 3 =-0-6 C yang diletakan pada titik asal koodinat 4. Dua bola kecil digantung sepeti gamba dibawah. Tiap bola memiliki massa 5 gam, dan bemuatan q. Panjang tali 30 cm. Kedua bola mencapai keseimbangan ketika θ=90 0. tentukan muatan masing-masing bola. 4

5 . Electic Field (E) The electic field stength of a chage (q) when an expeiment chage (q) is placed at distance of fom that chage can be detemined by the equation follows kq E E = electic field stength (N/C) Electic Flux Is defined as the numbe of electic field lines that piece a closed suface, that mathematically expessed by the following equation : EAcos electic flux (webe) θ = the angle between E with the nomal line of the plane Gauss s Law the numbe the electic field lines that penetate a closed suface is popotional with the amount of electic chage coveed by the closed suface, can be expessed by the equation as fallow q EAcos 0 The Application of Gauss s Law. Electic field stength between paallel chaged plates E chage density (C/m ) 0. Electic field stength by the chaged conducto ball kq E 5

6 Execise. what is the electic field stength at 0.5 mm fom a chage of +µc (7. x 0 0 N/C). at cone points of B and D of a squae ABCD ae placed a chaged paticle of +q. detemine the chage of paticle that must be located at point C so that the electic field at A is zeo 3. Two point chages consecutively +8 µc and + µc ae sepaated 5 cm fom each othe. Detemine the location of a poin fom +8 µc chage that its electic field stange is equal to zeo 4. To chage each of +.5 µc and -7 µc ae located 0 cm fom each othe. Detemine a) the electic field stength in the middle b) the foce exet upon the chage of +8 x 0 7 C in the middle 5. Two paticle A and B ae consecutively chage +0 µc and 45 µc and sepaated 5 cm. if C is placed between A and B. so that E c =0. detemine the location of C fom A 6. Pada gamba dibawah ini dimanakah letak titik yang kuat medannya nol? -q 7 cm +8q 7. A spheical conducto has adius 5 cm and chaged 30 µc with unifom distibution of chages in the suface. Detemine: a) the chage density in the ball suface b) the electic field stength at 5 cm fom the cante of the ball 6

7 c) the electic field stength in the suface d) the electic field stength at 8 cm fom the cante of the ball 8. Explain the definition of the following tems a) electic flux b) Gaussian suface c) Chage density 9. Explain why the value of E inside the conducto ball is zio 0. A conducto ball has adius of 0 cm. if its chage is C detemine : a) E at 5 cm in cante of the ball b) E at 0 cm in cante of the ball c) E at 5 cm in cante of the ball. Two opposite paallel plates chaged Q = 3 µc and the aea is 6 cm x.5 cm. detemine a) Chage density b) Electic field stength between the plates. hitunglah jumlah gais medan yang menembus bidang pesegi (sisi = 5 cm) bila vecto medan listik homogen sebesa 0 N/C 3. Sebuah kondukto keping sejaja yang tiap kepingnya bebentuk pesegi dengan panjang sisi 30 cm. Dibei muatan 7.08 µc yang belawanan jenis, hitung: a) Rapat muatan listik tiap keping b) Besa kuat medan listik dalam uang diantaa kedua keping 4. Sebuah kondukto bola beongga yang jaijainya 4 cm dibei muatan +0, µc. Titiktitik A, B dan C betuut-tuut jaaknya cm, 4 cm dan 6 cm dai pusat bola. Hitung kuat medan listik dititik A, B dan C 7

8 3. Electic Potential Electic potential is defined as the chage of potential enegy pe unit chage when an expeiment chaged is move between to point. Can be detemined by the following equation: kq V Electic potential enegy Is the multiply between electic potential with expeiment chage E p qv k qq0 E p Wok If an expeiment chage (q 0 )in the electic field of a souce chage (q) is moved fom position A to position B, then the value of wok equied is equal to the change of potential enegy (ΔE p ) ΔE p = W So that W q W kq0q ( ) 0 V B A Equipotential Planes W 0 Electic Potential by The Chaged Conducto Ball The electic potential inside the chaged conducto ball While the electic potential outside the ball kq V Electic Potential Between Two Chaged Paallel Plates kq V R R = Radius of te ball = Point distance to the cente of the ball V E. d V.d V. d 0 Mechanical Enegy Consevation Law qv mv qv mv 8

9 EXERCISE. Tentukan peubahan enegi listtik ketika sebuah elekton dalam atom hidogen (muatan e = -,60 x 0-9 C) begeak dai suatu keadaan teeksitasi pada =,00 x 0-0 m ke keadaa enegi teendahnya pada = 5 x 0 - m. Sebuah bola kecil dimuati +,00 x 0-6 C a. hitung beda potensial antaa kedudukan awal yang jauhnya 0,900 m dai muatan dan kedudukan akhi yang jauhnya 0,600 m dai muatan b. beapa peubahan enegi potensial yang tejadi jika bola lain bemuatan - 5,00 x 0-8 C digeakkan diantaa kedua kedudukan ini? c. apakah peubahan enegi potensial pada (b) betambah atau bekuang? 3. Dua buah muatan q = +,00 x 0-6 C dan q = -5,00 x 0-6 C tepisah sejauh 0,400 m. Tentukan potensial pada suatu titik ditengah-tengah antaa kedua muatan tesebut 4. Pada keempat sudut sebuah pesegi (sisi = 30 cm) diletakkan muatan-muata titik yang sama -6,0 µc. Hitung potensial listik dipusat pesegi itu 5. Poton yang begeak dai A ke B mempeoleh kecepatan x 0 5 m/s. Jika diantaa dua keping vakum, d = cm, dan massa poton =,6 x 0-7 kg, muatan poton,6 x 0-9 C, tentukan beda potensial keping sejaja ini 9

10 6. Beda potensial 4 kv dibeikan antaa ujung-ujung sebuah kondukto kepig sejaja yang tepisah sejauh 0 cm. Tentukan: a. kuat edan listik dalam uang anta keping b. beda potensial antaa titik yang bejaak 4 cm dai keping positif tehadap keping negatifnya 7. Muatan,75 x 0-8 C didistibusikan meata pada sebuah kondukto bola beongga yang diametenya 50 mm a. beapa potensial listik dikulit bola? b. beapa potensial listik pada tepat yang bejaak 50 mm dai pusat bola? c. Hitung enegi potensial sebuah muatan,5 x 0-5 C yang diletakkan 50 mm dai pusat bola 8. Sebuah elekton (muatan e ) diletakkan pada setiap dai kedelapan titik sudut dai sebuah kubus degan panjang usuk a, dan sebuah patikel (muatan +e) pada pusat kubus tesebut, hitunglah enegi potensial sistim 9. the electic potential at a point that has distance of fom chage Q is 300 volt. The electic field stength at that point is 800 N/C. detemine the amount of chage Q (.5 x 0-8 C ) 0. A conducto ball has diamete of 0 cm and is chaged 00 µc. detemine : a. electic potential at 5 cm fom the cente of the ball (9 x 0 6 volt) b. electic potential at 0 cm fom the suface of the ball (45 x 05 5 volt) 0

11 . what is the wok equied to move the positive chage of 0 C fom one point (V =0 volt) to anothe (V =60 volt)?. The potential diffeence between two paallel plates with equal and opposite chages is 400 volt within an empty cylinde. If the electons fom the negative plate ae acceleated towad positive plate with v 0 =0, then detemine the speed of electons when stike the positive plate (m e = 9. x 0-3 kg and e = -.6 x 0-9 C) 3. The electic potential at a point that has distance of cm fom a point chage is 0.4 volt. Detemine the electic potential at 8 cm fom the chage 4. In the cone points a squae ABCD locate the chages consecutively +4 µc. -4 µc, +4 µc and -4 µc. Detemine the electic potential at : a. the cente of the squae, if the side length is cm b. in the middle side between A and B 5. A chaged conducto ball (Q = 00 µc) has adius of 5 cm. detemine the wok equied to move an electon (e = -.6 x 0-9 C) fom the suface of the ball so that it is not influenced by the ball s chage

12 6. The ight tiangle ABC has the length AB = 4 cm and AC = 3 cm and at evey cone locates the electic chages of q A = +0-0 C, q B = -0-0 C and q C = -0-0 C, as shown the figue below, calculate the wok equied to move q C to D B D A C 7. An electon is shot by speed of 5000 m/s in paallel diection with electic field (E = 000 V/m). what is the geatest distance eached by the electon befoe it stop?

13 4. Capacitos Is n electonic component use fo stoing electic chage and electic enegy. Capacitance of Capacito (C) Capacitance of Capacito can be detemined by the equation as follows Q C V Accoding to gauss s Law plates capacito, the electic field stength between two plates can be detemine as follows With ε = ε 0 ε A 0 A C C d d. Electic Enegy in Capacito The enegy of capacito can be detemined by the equation blow: W CV QV Q C 3. Capacito Connection a. Seies Capacito Connection C C C... s C n b. Paallel Connection of Capacitos C C C... p C n 3

14 Execise. A paallel plates capacito has the aea of each plate cm and both ae sepaated 0. cm. if the chage at each plate is 4 µc and ε 0 = 8.85 x 0 - C /Nm detemine a. capacitance of capacito if the electic mateial is immesed between both plates (k = 4) b. potential diffeence between both plates. Two capacito 3 µc and 5 µc ae connected in seies and set at a voltage souce of 0 volt. Calculate the enegy stoed in that system 3. Two Capacitos C = 6 µc and C = 3µC ae connected in paallel and set at the voltage souce of 8 V, calculate a. substitute capacitance (C p ) b. chage of q and q c. voltage V and V 4. A capacito has the capacitance of 0.6 µf, it is chaged by voltage of volt. Calculate the chages stoed in the capacito 5. A capacito 6 µf is chaged so that the voltage become 5 volt, then it is connected with capacito 4 µf, calculate the voltage now 6. to stoe C chage is used the capacitos which each has capacitance of.5 µf and it is connected in paallel with potential diffeence of 00 volt. Calculate the sum of capacitos used 7. To make the capacitance in the figue below equal to C, detemine the elation between C and C 4

15 8. A capacito is given chages with voltage 00 volt. If the potential is educed to 90 volt, calculate the decease of enegy in the capacito 9. sebuah kapasito yang dimuati oleh bateai mv dapat menyimpan muatan 5.0 x 0 - C. Tentukan kapasitas kapasito tesebut 0. sebuah kapasito keping sejaja memiliki keping empat pesegi panjang dengan panjang 0 cm dan leba 8 cm, dipisahkan oleh jaak mm a. hitunglah kapasitasnya b. jika banyak muatan yang dipindahkan dai satu keping kekeping lainnya adalah 0.53 nc, beapa beda potesial kedua kepig tesebut itu?. sebuah kapasito tebentuk dai dua lempeng almunium yang luas pemukaannya masing-masing 00 cm dan dipisahkan oleh minyak silikon yang tebalnya.00 mm a. tentukan kapasitas kapasito ini b. tentukan muatan maksimum yang dapat disimpan dalam kapasito. sebuah kapasito keping sejaja, luas tiap keping 000 cm dan tepisah cm satu saa lain. Beda potensial diantaa keping 3000 volt bila beisi udaa, tetapi beda potensial itu menjadi 000 volt ketika diantaa keping disisipkan bahan dielectic. Hitungla : a. kapasitas mula-mula b. muatan q pada tiap-tiap keping c. kapasitas C setelah penyisipan bahan dielectic d. Pemitivitas elatif ε bahan dielectic e. pemitivitas ε bahan dielectic f. kuat medan listik mula-mula E 0 di antaa keping g. kuat medan listik E setelah penyisipan bahan dielektik 5

16 3. Sebuah kapasito keping sejaja tedii dai dua keping. Luas tiap keping 00 cm dan dipisahkan oleh celah udaa 4,0 cm a. hitnglah kapasitasnya b. jika kapasito dihubungkan pada bateai 500 v, beapakah muatan yang disimpan oleh kapasito itu? c. tanpa melepas bateai, suatu caian dengan ε =,50 dituangkan diantaa uang antakeping sehingga mengisi seluuh celah udaa, beapakah kapasitas sekaang? Beapakah tambahan muatan yang akan mengali dai bateai 500 volt menuju ke kapasito? 4. Tiga buah kapasito 0,0 µf dan 5,00 µf dan 4 µf disusun sei dan ujung-ujungnya dihubungkan ke tegangan sumbe volt a. kapasitas ekivalen b. muatan dan beda potensial tiap kkapasito 5. Tiga buah kapasito dengan kapasitas masing-masing 0.5 µf, 0,0 µf, 0,40 µf disusun paalel dan dihubungkan ke bateai 00 volt, tentukan a. kapasitas dan muatan ekivalen b. muatan dan beda potensial tiap kapasito 6. Dua kapasito 3 µf dan 5 µf disusun sei dan dihubungkan ke bateai volt. a. tentukan enegi yang tesimpan dalam sistem b. jika kedua kapasito itu disusun paalel, beapakah kenaikkan enegi yang tesimpan dala sistim? 6