2. Electrostatics. 2.1 What is electrostatics and electrostatic induction? 2.2 Explain coulomb s law of electrostatics

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1 . Eletostatis. What is eletostatis an eletostati inution? Eletostatis is a banh of siene ealing with eletiity at est i.e. stati eletiity. Nomally evey atom has an ual numbe of potons (ve hage) an eletons (ve hage).thus it is eletially neutal. Howeve, if by some metho we hange the numbe of eletons in the atom then it beomes eletially hage. hage boy has eithe an exess of eletons, whih auses the boy to be negatively hage o it has a efiieny of eletons, whih auses the boy to be positively hage. The simplest example is ubbing a glass o with a piee of silk. Fee eleton fom the glass o move to silk that makes the glass o positively hage an silk piee negatively hage. nothe metho to hage a neutal boy involves poximity between the unhage onuting boies. Suppose a positively hage boy X is bought nea a unhage boy Y, then the en of boy Y neae to boy X aquies positive hage. The negative hage on boy Y is alle the boun hage while the positive hage on Y is alle fee hage in figue.. The boun hages emain as long as boy Y is onnete to eath at that en. Similaly a negatively hage boy will inue positive hage on a boy nea it. Boy X Boy Y Boy X Boy Y Figue. hage boy moel Figue.hage boy moel Hee hage is inue only by neaness without any atual ontat. This phenomenon is alle eletostati inution. If two oppositely hage boies ae onnete with eah othe though a onuto, eletons will flow fom exess of hage (negatively hage boy) towas efiieny of hage (positively hage boy) onstituting eleti uent. This uent tansfes eletial enegy fom one point to anothe. On the othe han if two oppositely hage boies ae sepaate by some insulating meium whih pevents the movement of eleton, then hage will emain stati o stationay. This is alle stati eletiity.. Explain oulomb s law of eletostatis oulomb s fist Law It states that, like hages of eletiity epeals eah othe wheeas unlike hages of eletiity attat eah othe oulomb s seon Law The magnitue of foe between two hage boies is: Dietly popotional to the pout of hages Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5)

2 . Eletostatis Invesely popotional to the squae of the istane between them Depens upon the natue of the suouning meium Two hages an ae sepaate by istane. When these hages ae kept neae two eah othe it eates a foe. This foe may be attative o epulsive. Figue.3hage boy moel s pe oulomb se on law, F F K F 4π 9 F 9 Whee, F= Foe between two hage = hage on boy = hage on boy = Distane between two hage K= onstan t= = 9 4π = 8.85 Faa/Mete = Relative pemittivity of meium (fo i o aum, ).3 Define following tems (a) Eletial fiel Eleti fiel is imaginay lines of foe whih suouns hage boy. 9 Figue.4Eleti fiel Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5)

3 . Eletostatis Figue.5Eleti fiel between opposite hage Figue.6Eleti fiel between simila hage (b) () The haateistis of eleti lines of foe an be liste as follows: They always oiginate on a positive hage an teminate on negative hage. They always leave o ente a onuting sufae at ight angle to it. They neve oss o touh eah othe Lines of foe having the same ietion epel eah othe while those having opposite ietion attat eah othe. Eleti flux Total numbe of eleti lines of foes oiginating fom etain hage is alle eleti flux. Unit of eletial flux is oulomb(). Ψ Whee, Ψ Eleti flux hage Eleti flux ensity Eleti flux ensity at any point in a meium is eleti flux passing though unit aea at ight angle to the ietion of eleti fiel. Unit of eletial flux ensity is oulomb/mete. Ψ D Whee, D Eleti flux ensity Ψ Eleti flux oss setional aea () Eleti fiel intensity The stength of eleti fiel is alle eleti fiel intensity. Eletial fiel intensity is also known as eletial fiel stength. E whee, E Eleti fiel intensity oltage o potential Distane between hage Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5) 3

4 . Eletostatis (e) (f) (g) (h) (i) Unit of eletial fiel intensity is volt/mete. bsolute an elative pemittivity Pemittivity is the popety of a meium that affets the magnitue of the foe between two hages. Unit of pemittivity is faaay/mete. The geate the pemittivity of a meium plae between the hage boies, the lesse the foe between them. The atio of absolute pemittivity of some insulating mateial to the absolute pemittivity of ai o vauum (fee spae) is alle the elative pemittivity. Whee, bsolute(o atual) pemittivity of mateial Pemittivity of ai o vauum (fee spae)= 8.85 F / m Eletial potential Relative pemittivity of mateial Eletial potential at any point in an eletial fiel is efine as the wok one in binging a unit positive hage fom infinity to that point against the eleti fiel. Unit of eletial potential is volt (). W Whee, Eletial potential W Wok one hage Potential iffeene Potential iffeene is efine as the wok one in moving a unit positive hage within an eletial fiel fom a point of lowe potential to a point of highe potential. Unit of potential iffeene is volt (). Potential gaient It is efine as the ate of hange of potential o voltage with istane. Unit of potential gaient is volt/mete. g = X Whee, g Potential gaient hange in potential X hange in istane in the ietion of fiel Dieleti stength an beakown potential The maximum voltage that an be applie to a given mateial without ausing it to beak own. Unit of ieleti stength is k/mm o moe often k/m. It an be expess as a Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5) 4

5 . Eletostatis t Whee, = Beakown potential t = Thikness of the the ieleti.4 alue of ieleti stength of a ieleti eease with the inease in thikness. Explain Gauss s law Statement: The total numbe of the eleti flux oming out of a lose sufae is ual to the hage enlose ivie by the pemittivity Whee, Ψ Eleti flux Total hage on sufae bsolute pemitivity Ψ It is geneal law applie to any lose sufae. If a point hage of oulombs is plae at the ente of the sphee of aius then eleti flux emanating is oulomb an is pepeniula to the sphee. osθ sinθ θ Figue.7hage in ente an any point of sphee 3 4 Figue.8Numbe of hage on sufae Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5) 5

6 . Eletostatis If the point hage is plae at any point othe than the ente then flux emanating fom the point hage emains oulomb. Howeve the lines of foe will not be nomal to the sufae anymoe. This flux an be esolve into two omponent pepeniula omponents along the nomal sufae an hoizontal omponent pepeniula to it. The sum of all sinθomponents is foun to be zeo while sum of all osθ omponents is foun to be. Thus total flux ual to oulomb. If Thee ae a numbe of hages on sufae then by gauss s law, total flux emanating fom the sufae is Explain eletial potential at a point onsie a positive hage of oulombs plae in ai an at a istane x metes fom hage. x x Figue.9Eletial potential at a point The foe ating on the unit positive hage is given by F E 4π x Wok one in moving the unit hage though a small istane x towas is given by W W F ( x) 4π x ( x) The negative sign iniate that wok one is against the ietion of the eletial fiel. Theefoe, the total wok one in moving a unit positive hage fom infinity to a point metes away fom is givenby W W W 4π x W π x x 4 W 4 π x W 4 π x Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5) 6

7 . Eletostatis W 4 π W 4 π W 4 π (in meium) 9 W 9 (in vauum).6 Explain eletial potential of hage sphee Figue.hage sphee onsie an isolate sphee of aius mete plae in ai an aying a positive hage of oulombs whih is unifomly istibute ove its sufae. hages will behave like they ae onentate at ente of the sphee. Theefoe potential at any point metes ( > ) away fom the ente of sphee will have the same potential. ( in ai) 4π ll the point at istane metes fom the ente of sphee will have the same potential. Eleti flux o lines of foe ae always nomal to uipotential sufae. Potential at the point of the sufae of the sphee is given by 4π Fo any point within the sphee the potential will be ual to the potential at sufae of sphee. When hage is given to sphee it esies only on its oute sufae. Within the sphee, hage, flux an fiel intensity ae zeo. Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5) 7

8 . Eletostatis.7 Relationship between eletial flux ensity an eletial fiel intensity ssume one sphee have aius of. Point P is the ente point of sphee. P Figue.D an E at a point P in the eletial fiel Flux ensity at point P fom istane an be efine as below Flux D ea Φ 4π Eleti fiel intensity at point E The ating on unit positive hag e when plae at P 4π 4π Solve uation i an i E D D E D E D E D D E E i.8 What is apaito an apaitane? P is n aangement whee two onuting sufae ae sepaate by a laye of insulating meium is alle a apaito o a onense. apaitane is the popety of apaito to stoe enegy in fom of eleti hage. ( i) ( ii) Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5) 8

9 . Eletostatis The onuting sufae is alle plates an insulating mateial between is alle the ieleti. i, mia, glass, waxe pape, eami, et. ae some of the most wiely use ieletis. The shape of the onuting sufaes may be iula, spheial o ylinial. apaito is also alle a onense beause when potential iffeene is applie aoss two plates, sepaate by ieleti, the lines of foe ae onense into the spae between the plates. apaito stoes enegy in the fom of an exess of eletons on one plate an efiieny of eletons on the othe. The time of stoage may be in tems of nanoseons, milliseons, seons o minutes. Sometimes apaitos employe in powe iuits hol thei hage fo many hous ontinuously, although, the amount of hage may vay slightly. apaito s ability to hol hage is measue in faas. This is a vey lage unit. Mostly apaitos ae ate in miofaas o less. B B S S (a) (b) B B S S () () Figue.apaito with supply voltage paallel plate apaito with plates an B is onnete though a swith to a battey of volts. When swith is open thee is no hage on the plates i.e. the plates ae neutal. When the swith is lose in above, some fee eletons fom plate ae attate by the positive teminal of the battey. The efiieny of eletons on plate eates a positive hage on it. The eletons ae tansfee fom the positive teminal of the battey to the negative teminal, Then the negative teminal immeiately epels these eletons towas plate B, thus eating an exess of eletons thee. Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5) 9

10 . Eletostatis Thus a potential iffeene is establishe between the plates an B, whih ats as a ounte emf i.e. opposes the flow of eletons. The movement of eletons will ontinue till the potential iffeene between the two plates beomes exatly ual to the emf of the battey. When a apaito is fully hage, then the potential iffeene aoss its plates is ual to the voltage applie aoss its teminals uing haging. The plates of a hage apaito always ay ual an opposite hages i.e. an. Now if the swith is opene i.e. applie voltage is isonnete, the apaito plates an B will etain thei positive an negative hages espetively. If a potential iffeene of volts aoss a apaito s plate auses oulomb hage to aumulate on its plates, then it has been foun expeimentally that α Whee, hage on the apaito plates Potential iffeene between the plates apaitane Thus, apaitane is efine as the atio of the hage on apaito plates to the potential iffeene aoss its plates. If = volt, = oulomb then = faa. Hene a apaito has a apaitane of faa if it aquies a hage of oulomb on its plates when a potential iffeene of I is applie aoss its plates. s mentione ealie faa is a vey lage unit. Nomally, apaitos ae ate in tems of miofaas o piofaas..9 Explain seies an paallel onnetion of apaito Seies onnetion of apaito Paallel onnetion of apaito Figue.3Seies ombination of apaito Figue.4Paallel ombination of apaito Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5)

11 . Eletostatis s pe KL, If n apaito ae onnete in seies alue of uivalent apaitane of seies iuit is smalle than the smallest value of iniviual apaitane of iuit.. apaitane of a paallel plate apaito (a) n s pe KL, If n apaito ae onnete in paallel 3... alue of uivalent apaitane of paallel iuit is bigge than the biggest value of iniviual apaitane of iuit. apaitane of paallel plate apaitane with unifom ieleti meium n Figue.5apaitane of apaito with unifom ieleti meium Two plates of apaito ae sepaate by istane, plate aea is, hage on plate is. Eleti flux ensity D Eleti fiel stength E n D E iii Solve uation ( i),( ii) an( iii) i ii Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5)

12 . Eletostatis D Whee, hage on plate Distane between plate Relative pemittivity of mateial (b) apaitane of paallel plate apaitane with omposite ieleti meium ase of omposite apaito Figue. 6ase of omposite apaito Figue.7Equivalent iuit of ase omposite apaito Hee an ae in seies, Whee, ea of plate Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5)

13 . Eletostatis Thikness of ieleti mateial Thikness of ieleti mateial Relative pemittivity of ieleti mateial Relative pemittivity of ieleti mateial apaitane ue to ieleti mateial apaitane ue to ieleti mateial ase of omposite apaito Figue.8ase of omposite apaito Figue.9Equivalent iuit of ase omposite apaito Hee an ae in paallel, Whee, ea of ieleti mateial ea of ieleti mateial Thikness of ieleti mateial Relative pemittivity of ieleti mateial Relative pemittivity of ieleti mateial apaitane ue to ieleti mateial apaitane ue to ieleti mateial ase3 of omposite apaito Hee an ae in seies, ' Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5) 3

14 . Eletostatis ' ' 3 3 Figue.Thi type of omposite apaito Figue.Equivalent iuit thi type of omposite apaito ' ' Hee an ae in paallel, ' ' Whee, ea of ieleti mateial& ea of ieleti mateial3 Thikness of ieleti mateial Thikness of ieleti mateial Thikness of ieleti mateial3 Relative pemittivity of ieleti mateial Relative pemittivity of ieleti mateial Relative pemittivity of ieleti mateial3 apaitane ue to ieleti mateial apaitane ue to ieleti mateial apaitane ue to ieleti mateial Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5) 4

15 . Eletostatis Equivalent apaitane of an ' Equivalent apaitane of the iuit. Explain apaitane of a multiplate apaito The apaitane of a apaito an be inease by using a ieleti having high elative pemittivity an eeasing the istane between the plates. This ieleti mateial is vey ostly an while euing the gap between the plates the ieleti stength also must be onsiee. nothe metho is to inease the plate aea, but this leas to bulky size. To avoi all these iffiulties a multiplate onstution is employe Dieleti Meium B B 3 Figue.apaitane of multiplate apaito Figue.3Equivalent iuit of multiplate apaito multi plate apaito is built up of a numbe of metal plates of same imensions sepaate by a ieleti mateial. The altenate plates ae onnete togethe. if thee ae n plates, then thee ae (n ) spaes fille with the ieleti. This is uivalent to (n ) simple paallel plate apaitos. The total apaitane of n plate apaito is n apaitane between one pai of plates n Whee, oss setion aea of eah plate Thikness of the ieleti between eah pai of plates Relative pemittivity of ieleti mateial. Explain types of apaito (a). Fixe apaitos ae lassifie on the basis of the ieleti use. Pape apaito The metal plates ae mae up of aluminum foil inteleave with pape impegnate with wax o oil. Suh apaitos ae ommonly use in powe iuits of househol applianes, bypass an oupling iuits et. Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5) 5

16 . Eletostatis (b) () () (e) (f) (g) Plasti film apaito These ae simila in onstution to the pape insulate apaitos exept that tanspaent plasti foil is use as a ieleti instea of pape. Mia apaito It onsists of altenate layes of mia an metal foil lampe tightly togethe. Mia is an exellent ieleti an an easily be mae into thin hips. It is use fo making stable an auate apaitos. Mia is elatively ostlie. So it is mainly use fo making apaitos use in the high fueny iuits whee the ieleti loss shoul be least. eami apaito thin eami ieleti is oate on both the sies with metal. stak of suh layes is mae. Eah laye is sepaate fom the next by moe eami. The plates ae onnete to the eletoes an a suitable oating is one ove the apaito. They geneally have small apaitane values of pf to µf. The woking voltage may be up to a few thousan volts but the leakage esistane is also high (about MΩ). eami apaitos ae useful at high tempeatues. The basis of eami mateial is mainly baium titanate whose elative pemittivity is above 6. This is vey small sepaation between the plates whih esults in the small size apaitos. It has a low powe fato whih eeases with the inease in fueny. It is useful fo shot wave aio wok. Polyeste apaito Polyeste is manufatue in vey thin films an the metal is eposite on one sie. Two films ae then olle togethe like pape apaitos. Due to thei small size, atings annot be pinte on the sufae. Geneally, they ae olo oe like esistos. These apaitos an opeate at high voltages of about a few thousan volts. Eletolyti apaito The insulation esistane of this apaito is vey low an it is suitable only fo those iuits whee the voltage aoss the apaito oes not evese its ietion. Hene they an wok only with supply. Eletolyti apaitos ae mainly use whee lage values of apaitanes ae uie, eg. Smoothing iuits in the aio wok. Tantalum eletolyti apaito These apaitos ae small in size as ompae to the eletolyti apaitos of the same ating. One plate onsists of sintee tantalum powe oate with an oxie laye whih ats as the ieleti. ase of bass, oppe o sometimes even silve foms the othe plate. Layes of manganese ioxie an gaphite fom the eletolyte. Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5) 6

17 . Eletostatis.3 Explain haging an ishaging of apaito haging of apaito Dishaging of apaito R R R R Figue.4haging of apaito pply KL in iuit, R R ir q R t R t t t t Multiply min us sign both the sie t log K ( i) When, t, log K ( ii) Solve uation () an () log log log log log e e Figue.5Dishaging of apaito pply KL in iuit, R ir q R t R t t t t log log K ( i) When, t, log K ( ii) Solve uation ( i) an ( ii) log log log log e e Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5) 7

18 . Eletostatis lso, ( e ) q i t ( ) i t i ( ( e )) t i ( e ) t i e i e i e R m i i e q lso, i t ( ) i t i t i ( e ) t i e i e R m i I e λ.63 v v.37 t λ t Figue.6haging voltage of apaito I Figue.8Dihaging voltage of apaito λ O.37 Im t i.37 λ Figue.7haging uent of apaito Im Figue.9Dihaging uent of apaito Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5) 8

19 . Eletostatis.4 Explain enegy stoe in apaito When a potential iffeene is applie aoss a apaito, the eletons ae tansfee fom one plate to the othe plate though the battey an the apaito is hage. The haging of a apaito involves expenitue of enegy by the haging ageny. This enegy is stoe in the eletostati fiel set up in the ieleti meium between the plates of the apaito. On ishaging the apaito, the eletostati fiel ollapses an the stoe enegy is elease. To begin with, when the apaito is unhage, little wok is one in tansfeing hage fom one plate to anothe. But futhe installments of hage have to be aie against the epulsive foe ue to the hage aleay ollete on the apaito plates. Let us fin the enegy spent in haging a apaito of apaitane to a voltage. Suppose at any state of haging, the potential iffeene aoss the plates is v volts. By efinition it is ual to the wok one in shifting one oulomb of hage fom one plate to anothe. Enegy stoe in apaito at any instant, w w w vq v v v v Total wok one in aising the potential iffeene of unhage apaito to volt is, w v v v W W This wok one o enegy is stoe in eletostati fiel setup in the ieleti meium plae between the plates of apaito. Piyush Rupala, EE Depatment Elements of Eletial Engineeing (5) 9

AVS fiziks. Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES

AVS fiziks. Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES ELECTROMAGNETIC THEORY SOLUTIONS GATE- Q. An insulating sphee of adius a aies a hage density a os ; a. The leading ode tem fo the eleti field at a distane d, fa away fom the hage distibution, is popotional