5. ELECTROSTATICS. Synopsis :

Transcription

1 5. ELECTROSTATICS Synopsis :. Stuy of stationay electic chages at est is known as electostatics.. Electic Chage : i) It is a funamental popety of matte an neve foun fee. ii) Thee ae two kins of chages namely positive an negative. If a boy has excess of electons, it is sai to be negatively chage an if it is eficient in electons, it is sai to be positively chage. iii) Benzamin Fankline intouce the concept of positive an negative chages. iv) Repulsion is the sue test fo the etection of a chage. v) In S.I. system the unit of chage is coulomb. vi) Chage is scala uantity. vii) Like chages epel an un-like chages attact. viii) Chage is conseve. It can neithe be ceate no estoye. It can only be tansfee fom one object to othe. ix) Chage is uantise. The smallest chage is associate with electon ( ) an poton () is.6 9 coulomb. x) All chages in natue exist as integal multiples of electon chage. n.e. n Intege xi) A coulomb is euivalent to a chage of electons. xii) When a boy is positively chage, its mass slightly eceases xiii) When a boy is negatively chage, its mass slightly inceases. xiv) In the case of a conucto, its chage speas ove the entie oute suface an in the case of an insulato, its chage is localise xv) Chage given to a conucto always esies on the oute suface of the conucto only. 3. Chaging of boies : i) The pocess of making a neutal boy into a chage boy is known as electification ii) Electification is univesal phenomenon iii) A boy can be chage by any one of the following thee ways : (a) fiction (b) contact an (c) electostatic inuction 4. Chaging by fiction : i) The electicity (i.e., tansfe of electons) that is pouce ue to fiction is calle fictional electicity ii) When we ub two neutal boies, thee will be some tansfe of electons fom one boy to the othe ue to stuctual moifications because of the fictional foces acting on them. iii) In this metho one of the boies acuies a negative chage while the othe gets a positive chage, both of which ae eual in magnitue.

2 Eg: a) When a glass o is ubbe with silk cloth, glass acuies positive chage an silk cloth acuies negative chage. Electons ae emove fom glass o an ae ae to silk cloth. b) When an ebonite o is ubbe with fu cloth, ebonite o acuies negative chage an fu cloth acuies positive chage. Electons ae tansfee fom fu cloth to ebonite o. iv) The list of substances calle electic seies given below is aange in such a manne that if any two of them ubbe togethe, the one occuing ealie woul be positively chage.. Glass. Flannel 3. Wool 4. Silk 5. Sealing wax 6. Ha metal 7. Ha ubbe 8. Resin 9. Sulphu, etc. Eg: If we select glass an silk, glass will acuie a positive chage while silk will get a negative chage when glass o is ubbe with silk 5. Chaging by contact : i) A neutal boy can be chage by making contact with a chage boy. ii) Hee the boy will acuie a chage that is the same as that of the chaging boy. iii) Thus by contact a simila chage is fome on both the boies. iv) In this metho fist boy s chage eceases. 6. Chaging by electostatic inuction : i) Inuction always pecees attaction ii) Polaisation of chages in a boy when a chage boy is pesent nea that is calle inuction. iii) In inuction, a chage boy is bought nea an unchage boy. Then the unchage boy acuies a chage opposite in sign to that of the chage boy. Inuce chage on ielectic slab of ielectic constant K is Fo metals K α.. K iv) Without a ecease in the chage of the boy, which inuces by the metho of inuction, boies can be chage continuously. 7. Conuctos, insulatos an semiconuctos: i) A boy in which electic chage can easily flow though is calle conucto (e.g. metals). ii) A boy in which electic chage cannot flow is calle insulato o ielectic. (e.g. glass, wool, ubbe, plastic, etc.) iii) Substances which ae intemeiate between conuctos an insulatos ae calle semiconuctos.(e.g. silicon, gemanium, etc) 8. Electoscope : i) An electoscope is use to etect the chage on a boy. ii) Pith ball electoscope is use to etect a chage an to know the natue of the chage.

3 iii) Gol leaf electoscope which was invente by Bennet etects a chage an the natue of the chage an etemines the uantity of the chage. 9. Coulomb s law : i) The foce of attaction o epulsion between two chage boies is iectly popotional to the pouct of thei chages an invesely popotional to the suae of the istance between them. ii) It acts along the line joining the two chages consiee to be point chages. iii) F α iv) F oε (o) F (o) ok F a) whee ε is absolute pemittivity, K o ε is the elative pemittivity o specific inuctive capacity an ε o is the pemittivity of fee space. b) K o ε is also calle as ielectic constant of the meium in which the two chages ae place. v) a) Relative pemitivity of a mateial Foce between two ch ag es in ai ε K Foce between the same ch ag es in the meium at the same is tan ce ε F F a m b) Fo ai K c) Fo metals K infinity ) Foce between chages epens upon the natue of the intevening meium, whee as gavitational foce is inepenent of intevening meium. vi) Fo ai o vacuum, F. o since fo ai o vacuum, ε K vii) The value of is eual to 9x 9 Nm /C. o viii) A coulomb is that chage which epels an eual chage of the same sign with a foce of 9x 9 N when the chages ae one mete apat in vacuum. ix) The value of ε o is 8.86 C /Nm (o) 8.86 Fm x) Coulomb foce is consevative mutual an intenal foce. xi) Coulomb foce is tue only fo static chages.. Coulomb s law in vecto fom : ) F ˆ F F 4π ; F F Hee F is foce exete by on an F is foce exete by on. ) Coulomb s law hols fo stationay chages only which ae point size. 3

4 3) This law obeys Newton s thi law ( ie ) F F. Electostatics. Foce on a chage paticle ue to a numbe of point chages is the esultant of foces ue to iniviual point chages i.e. F F F... F 3. i) If the foce between two chages in two iffeent meia is the same fo iffeent sepaations, F constant. K 4π ii) K constant o K K iii) If the foce between two chages sepaate by a istance in vacuum is same as the foce between the same chages sepaate by a istance in a meium, K k 3. a) Two ientical conuctos having chages an ae put to contact an then sepaate, then each have a chage eual to. If the chages ae an, then each have a chage eual to. b) Two spheical conuctos having chages an an aii an ae put to contact an then sepaate then the chages of the conuctos afte contact ae ( ) & ( ). c) The foce of attaction o epulsion between two ientical conuctos having chages an when sepaate by a istance is F. If they ae put to contact an then sepaate by the same istance the new F ( ) foce between them is F 4 If chages ae an then F ( ) F 4 ) Between two electon sepaate by a cetain istance Between two potons sepaate by a cetain istance Between a poton an an electon sepaate by a cetain istance. Electical foce Gavitational foce Electical foce Gavitational foce 4 36 Electical foce 39 Gavitational foce e) The elationship between velocity of light, pemeability of fee space an pemittivity of fee space is given by the expession c / ( μ oε o ). f) If two ientical balls each of mass m ae hung by silk thea of length fom a same hook an cay simila chages then. g) The istance between balls 4π mg h) The tension in the thea ( F ) ( mg) / 3 4

5 i) If total system is kept in space then angle between theas is 8 an tension in thea is given by T 4π 4 4. A chage Q is ivie into an (Q ). Then electostatic foce between them is maximum when (o) Q. Q ( ) 5. Electic fiel an electic intensity : i) The space aoun an electic chage in which its influence can be felt is known as electic fiel. ii) The intensity of electic fiel (E) at a point is the foce expeience by a unit positive chage place at that point. iii) It is a vecto uantity. iv) E F/, unit of E is NC o Vm v) Due to a point chage, the intensity at a point units away fom it is given by the expession E NC. Anothe unit is volt/mete. vi) The electic fiel ue to a positive chage is always iecte away fom the chage. vii) The electic fiel ue to a negative chage is always iecte towas the chage. viii) The intensity of electic fiel at any point ue to a numbe of chages is eual to the vecto sum of the intensities pouce by the sepaate chages. 6. Foce expeience by a chage Q in an electic fiel. F QE whee E is the electic intensity. i) If Q is positive chage, the foce F acts in the iection of E F QE. Acceleation a m m ii) If Q is negative chage, the focef acts in a iection opposite to E F QE Acceleation a m m iii) A chage in an electic fiel expeiences a foce whethe it is at est o moving. iv) The electic foce is inepenent of the mass an velocity of the chage paeticle, it epens upon the chage. v) A poton an an electon in the same electic fiel expeience foces of samemagnitue but in opposite iections. vi) Foce on poton is acceleating foce whee as foce on electon is etaing foce. If the poton an electon ae Acceleation of P oton mass of electon initially moving in the iection of electic fiel. Re taation of electon mass of poton 7. Dielectic Stength : It is the minimum fiel intensity that shoul be applie to beak own the insulating popety of insulato. i) Dielectic stength of ai 3 6 V/m Dielectic stength of Teflon 6 6 Vm ii) The maximum chage a sphee can hol epens on size an ielectic stength of meium in which sphee is place. 5

6 iii) The maximum chage a sphee of aius can hol in ai 4π ielectic stength of ai. 8. When the electic fiel in ai excees its ielectic stength ai molecules become ionise an ae acceleate by fiels an the ai becomes conucting. 8. Electic lines of foce : i) Line of foce is the path along which a unit ve chage, acceleates in electic fiel. ii) The tangent at any point to the line of foce gives the iection of the fiel at that point. iii) Two lines of foce neve intesect. iv) Numbe of lines of foce passing nomally though unit aea aoun a point is numeically eual to E, the stength of the fiel at the point. v) Lines of foce always leave o en nomally on a chage conucto. vi) Electic lines of foce can neve be close loops. vii) Lines of foce have tenency to contact longituinally an exet a foce of epulsion on one anothe lateally. viii)if in a egion of space thee is no electic fiel, thee will be no lines of foce. Insie a conucto thee cannot be any line of foce. ix) Numbe of lines of foce passing nomally though unit aea aoun a point is numeically eual to E. x) In unifom fiel, lines of foce ae paallel to one anothe. Unifom fiel Magnitue is Diection is Both magnitue not constant not constant an not constant Non unifom magnetic fiel 9. Diffeence between electic lines of foce an magnetic lines of foce : i) Electic lines of foce neve fom close loops while magnetic lines ae always close loops. ii) Electic lines of foce o not exist insie a conucto but magnetic lines of foce may exist insie a magnetic mateial.. Motion of a chage paticle in an electic fiel. i) If a chage paticle of chage Q is place in an electic fiel of stength E, the foce expeience by the chage paticle EQ. EQ ii) The acceleation of the chage paticle in the electic fiel, a m EQ iii) The velocity of chage paticle afte time t is V at t if the initial velocity is zeo. m EQ iv) The istance tavelle by the chage paticle is S at m t if the initial velocity is zeo 6

7 v) When a chage paticle is pojecte into a unifom electic fiel with some velocity pepenicula to the fiel, the path tace by it is paabola. vi) The tajectoy of a chage paticle pojecte in a iffeent iection fom the iection of a unifom electic fiel is a paabola. vii) When a chage paticle of mass m an chage Q emains suspene in an vetical electic fiel then mgeq. viii)when a chage paticle of mass m an chage Q emains suspene in an electic fiel, the numbe of funamental chages on the chage paticle is n then mg E(ne) mg n Ee xi) The bob of a simple penulum is given ve chage an it is mae to oscillate in vetically upwa electic fiel, then the time peio of oscillation is T π EQ g m x) In the above case, if the bob is given a ve chage then the time peio is given by T π EQ g m xi) A chage paticle of chage ±Q is pojecte with an initial velocity u making an angle θ to the hoizontal in an electic fiel iecte vetically upwa. Then usinθ a) Time of flight EQ g m b) Maximum height c) Range u u sinθ EQ g m sin g θ EQ m xii) Density of electic fiel insie a chage hollow conucting sphee is zeo xiii) A sphee is given a chage of Q an is suspene in a hoizontal electic fiel. The angle mae by the EQ sting with the veticle is, θ tan mg xiv) The tension in the sting is ( EQ) (mg) xv) A bob caying a ve chage is suspene by a silk thea in a vetically upwa electic fiel, then the tension in the sting is, T mg - EQ. xvi) If the bob caies ve chage, tension in the sting is T mg EQ. Suface chage ensity (σ): i) The chage pe unit aea of a conucto is efine as suface chage ensity. 7

8 total chage ii) σ, when A m then σ A aea iii) Its unit is coulomb/ mete an its imensions ae ATL. iv) It is use in the fomulae fo chage isc, chage conucto an infinite sheet of chage etc. v) σ σ i.e. σ vi) σ is maximum at pointe sufaces an fo plane minimum. vii) σ epens on the shape of the conucto an pesence of othe conuctos an insulatos in σ max vicinity of the conucto. σ min viii) σ is maximum at the cones of ectangula laminas an at the vetex of conical conucto.. Electic flux : σ min i) The numbe of electic lines of foce cossing a suface nomal to the aea gives electic flux φ E. nˆ θ E s φ E s cosθ φ φ E s E nˆ nˆ E Electostatics sufaces it is σ max the ii) Electic flux though an elementay aea s is efine as the scala pouct of aea an fiel. φ E. E.s Es cosθ iii) φ E.s E iv) Flux will be maximum when electic fiel is nomal to the aea (φ Es) v) Flux will be minimum when fiel is paallel to aea (φ t ) vi) Fo a close suface, outwa flux is positive an inwa flux is negative. 3. Gauss s Law : i) The total flux linke with a close suface is (/ ) times the chage enclose by the close suface. E.s ii) A point chage is place insie a cube of ege a. The flux though each face of the cube is 4. Electic potential (V): 8 6. ) Electic potential at a point in a fiel is the amount of wok one in binging a unit ve chage fom infinity to the point. ) It is eual to the Electic potential enegy of unit ve chage at that point. 3) It is a scala

9 4) S.I unit is volt 5) Potential at a istance ue to a point chage in ai o vacuum is V 6) V E.x v 7) E (o) V E x 8) A positive chage in a fiel moves fom high potential to low potential whee as electon moves fom low potential to high potential when left fee. 9) Wok one in moving a chage though a potential iffeence V is W V joule ) Gain in the Kinetic enegy ; mv V V ) Gain in the velocity v m 5. Euipotential suface ) A suface on which all points ae at the same potential ) Electic fiel is pepenicula to euipotential suface 3) Wok one in moving a chage on euipotential suface is zeo. 6. In the case of a hollow chage sphee.. ) Intensity at any point insie the sphee is zeo. ) Intensity at any point on the suface is same an it is maximum E 3) Outsie the sphee E.. istance fom the cente E R 4) It behaves as if the whole chage is at its cente. 5) Electic fiel Intensity in vecto fom E. 3 o E. ˆ 6) The esultant electic fiel intensity obey s the pinciple of supeposition. E E E... E 3 7. In the case of hollow chage sphee ) The potential at any point insie the sphee is same as that at any point on its E suface V. R ) It is an euipotential suface. 3) Outsie the sphee, the potential vaies invesely as the istance of the point fom the cente. V. 9

10 Note: Insie a non conucting chage sphee electic fiel is pesent. Electic intensity insie the sphee Q E. 3 R Hee is the istance fom the cente of sphee. E 8. Electon volt : i) This is the unit of enegy in paticle physics an is epesente as ev. ii) ev.6x -9 J. 9. Chage paticle in electic fiel : a) When a positive test chage is fie in the iection of an electic fiel, i) it acceleates, ii) its kinetic enegy inceases an hence iii) its potential enegy eceases. b) A chage paticle of mass m caying a chage an falling though a potential V acuies a spee of V/ m. 3. Electic ipole: i) Two eual an opposite chages sepaate by a constant istance is calle electic ipole. P. l. ii) Dipole moment (P ) is the pouct of one of the chages an istance between the chages. It is a vecto iecte fom negative chage towas the positive chage along the line joining the two chages. iii) The toue acting on an electic ipole place in a unifom electic fiel is given by the elation τ P x E i. e., τ PEsin θ, whee θ is the angle between P an E. iv) The electic intensity(e) on the axial line at a istance '' fom the cente of an electic ipole is P P E an on euatoial line, the electic intensity (E). 3/ ( ) ( ) l l v) Fo a shot ipole i.e., if l <<, then the electic intensity on axial line is given by P E. 3 vi) Fo a shot ipole i.e., if l P E. 3 <<, then the electic intensity on euatoial line is given by P vii) The potential ue to an electic ipole on the axial line is V ( l any point on the euatoial line it is zeo. viii) Two unlike eual chages Q an Q ae sepaate by istance ) The net electic potential is zeo on the pepenicula bisecto of the line joining the chages. ) The bisecto is euipoptential an zeopotential line. 3) Wok one in moving a chage on this line is zeo. ) an at Q Q

11 4) Electic intensity at any point on the bisecto is pepenicula to the bisecto. 5) Electic intensity at any point on the bisecto paallel to the bisecto is zeo. 3. Electic potential enegy : i) A chage place in an electic fiel possesses potential enegy an is measue by the wok one in moving the chage fom infinity to that point against the electic fiel. ii) If two chages an ae sepaate by a istance, the P.E. of the system is U iii) If two like chages (two potons o two electons) ae bought towas each othe, the P.E of the system inceases. iv) If two unlike chages (a poton an an electon ) ae bought towas each othe, the P.E. of the system eceases. v) If thee chages, an 3 ae situate at the vetices of a tiangle (as shown in the 3 figue), the P.E. of the system is U U U 3 U vi) If fou chages,, 3 an 4 ae situate at the cones of a suae as shown in the figue, P.E of the system vii) In the fiel of a chage Q, if a chage is move against the electic fiel fom a istance a to a istance b fom Q, the wok one W is given by Q Q Q Q a b W ( Vb Va ) b a πε b a 4 ab o b) Due to two issimila chages : o o 3. Combine fiel ue to two point chages a) Due to two simila chages : i) If chages an ae sepaate by a istance, null point ( whee esulting fiel intensity is zeo) is fome on the line joining those two chages. ii) null point is fome with in the chages. iii) null point is locate neae to weak chage. iv) If x is istance of null point fom, (weak chage) then x ( x) x x Hee an ae like chages / o

12 i) If an ae unlike chages then null point is fome on the line joining two chages. x x ii) null point is fome out sie the chages. iii) null point is fom neae weak chage. iv) x is the istance of null point fom (weak chage) then x / x ( x) In the above fomulae / is numeical atio of chages c) Zeo potential point ue to two chages : i) If two unlike chages an ae sepaate by a istance, the net potential is zeo at two points on the line joining them. ii) one in between them an the othe outsie the chages. iii) both the points ae neae to weak chage ( ). x y (fo point, with in the chages) ( x) P P y x (fo point,out sie the chages) ( y) Hee is numeical value of stong chage x ; y ) ue to two simila chages zeo potential point is not fome. 33. Euipotential suface: a) The suface which is the locus of all points which ae at the same potential is known as euipotential suface b) No wok is euie to move a chage fom one point to anothe on the euipotential suface. c) No two euipotential sufaces intesect ) The iection of electic lines of foce o iection of electic fiel is always nomal to the euipotential suface. e) Insie a hollow chage spheical conucto the potential is constant. This can be teate as euipotential volume. No wok is euie to move a chage fom the cente to the suface. f) Fo an isolate point chage, the euipotental suface is a sphee. i.e. concentic sphees aoun the point chage ae iffeent euipotential sufaces.

13 g) In a unifom electic fiel any plane nomal to the fiel iection is an euipotential suface. h) The spacing between euipotential sufaces enables us to ientify egions of stong an weak fiel. V E E P Q R E P < E Q < E R 4V 3V V V 34. Electical capacity : i) Electical capacity of a conucto is its ability to stoe electic chage. ii) The potential acuie by a conucto is iectly popotional to the chage given to it i.e., V Q. i.e., Q V o Q CV whee the constant of popotionality C is calle the electical capacity of the conucto. iii) Thus the capacity of a conucto is efine as the atio of the chage to the potential. iv) Its SI unit is faa. v) milli faa ( mf) -3 faa mico faa ( μ F) -6 faa pico faa ( pf) - faa vi) The capacity of a spheical conucto in faa is given by C vii) If we imagine Eath to be a unifom soli sphee then the capacity of eath 3 64 C R 7μ F mf Dielectic mateials, Pola an non pola molecules :, whee aius of the conucto. a) Dielectic mateial : Any mateial that o not allow the electical chages to easily pass though them is calle insulato o ielectic mateial o simply a ielectic. Dielectic is a technical tem fo an insulato. b) Non -pola molecule : i) In cetain kin of mateials, oinaily the molecules will have symmetic chage istibutions. ii) Such kin of molecules ae calle non-pola molecules. iii) In the absence of any extenal electic fiel, a non-pola molecule will have its cente of positive chage coinciing with cente of negative chage. c) Pola molecule : i) Cetain ielectics like wate, hyogenchloie an alcohol ae mae of molecules that have a non unifom istibution of electic chage. 3

14 ii) In such molecules, the positive chage cente will not coincie with the negative chage cente, even in the absence of any extenal fiel. iii) The molecules ae polaize even in the absence of any extenal electic fiel. iv) Such kin of molecules ae calle Pola molecules. 36. Paallel plate Capacito : i) Conense (usually, a combination of two conuctos) is a evice by means of which lage amount of chage can be stoe at a given potential by inceasing its electic capacity. ii) Capacitance of a capacito o conense is the atio of the chage on eithe of its plates to the potential iffeence between them. ε iii) Capacity of a paallel plate conense without meium between the plates C A A aea of each plate ; istance between the plates ε iv) With a meium of ielectic constant K completely filling the space between the plates C K A v) The ielectic constant of a ielectic mateial is efine as the atio of the capacity of the paallel plate conense with the ielectic between the plates to its capacity with ai o vacuum between the plates. C Capacity of the conense with ielectic meium between plates K C Capacity of the same conese with ai as meium between plates vi) When a ielectic slab of thickness t is intouce between the plates ε A t t k ε A t k C vii) In this case the istance of sepaation eceases by t an hence the capacity inceases k viii) To estoe the capacity to oiginal value the istance of sepaation is to be incease by t. k ε ix) a) If a metal slab of thickness t is intouce between the plates C A because fo metals K is infinity. t b) If a numbe of ielectic slabs ae insete between the plates, each paallel to plate suface, then euivalent capacity. A C. t t... tn K K Kn If those slabs completely fill up the gap between the plates leaving without any ai gap, ε A C. t t t... n K K Kn x) In a paallel plate capacito, the electic fiel at the eges is not unifom an that fiel is calle as the finging fiel. xi) Electic fiel between the plates is unifom electic intensity E chage ensity on the plates Q/A. σ ε Q Aε Q C. Hee σ is the suface 4

15 xii) Potential iffeence between the plates V E. Q ε A. Q CV xiii) Foce on each plate F EQ C Q ε A ε AE xiv) Enegy stoe pe unit volume of the meium ε E 37. Combination of Conenses: i) When conenses ae connecte in seies ) All plates have the same chage in magnitue ) Potential iffeences between the plates ae iffeent 3) V : V : V 3 : : C C C3 4) Euivalent capacity is C then, C C C C3 C C C 3 5) The euivalent capacity is less than the least iniviual capacity 6) Enegies of the conenses E : E : E 3 : : C C C3 7) Total enegy of the combinatione E E 3. ii) When conenses ae connecte in paallel ) P.D. acoss each conense is same ) Chage of each conense is iffeent Q : Q : Q 3 C : C : C 3 3) Euivalent capacity of the combination C C C C 3 4) The euivalent capacity is geate than the geatest iniviual capacity 5) Enegies of the conenses E : E : E 3 C C C 3 C : C : C 3 6) Total enegy of the combinatione E E 3 iii) When n ientical conenses each of capacity C ) Combine in seies, the effective capacity C s C/n ) Combine in paallel, the effective capacity C p nc. 3) Ratio of the effective capacities C s :C p : n iv) Mixe goup : If thee ae N capacitos each ate at capacity C an voltage V, by combining those we can obtain effective capacity ate at C an voltage V. Fo this n capacitos ae connecte in a ow an m such ows ae connecte in paallel. V nc Then n an m whee mn N V C C C 5 V V V

16 v) If C p an C s ae the euivalent capacities of two capacitos of capacity C an C in paallel an seies espectively then C CP Cp 4CPCS an C C P CP 4CPCS vi) Two capacitos ae connecte in paallel to a battey as shown in the figue. VC VC i) V ii) V C C C C vii) Two capacitos ae connecte in paallel to a battey as shown in the figue. C C i) ii) C C C C viii) If n ientical capacitos each of capacity C ae connecte in a suae then 4C a) The esultant capacity between any two ajacent cones A an B 3 V b) The esultant capacity between any two opposite cones A an C C V ix) If n ientical capacitos each of capacity C ae connecte in a polygon then nc a) The esultant capacity between any two ajacent cones n 4 C b) The esultant capacity between any two opposite cones. n x) a) If n ientical capacitos ae given then they can be connecte in n iffeent ways by taking all the conenses at a time (n > ). b) In n iffeent capacitos ae given then they can be connecte in n iffeent ways by taking all the conenses at a time. xi) In a paallel plate capacito, if n simila plates at eual istance ae aange such that altenate plates ( n )ε A ae connecte togethe, the capacitance (C) of the aangement is ( n )ε AK fo ai o vacuum an it becomes in a ielectic meium of P ielectic constant K. 38. Types of conenses : Capacitance of a vaiable capacito can be vaie gaually by vaying the effective aea inclue between the plates. a) Vaiable conense, multiple conense, pape conense, electolytic conense etc, ae the iffeent types of conenses. b) Vaiable capacito : i) In vaiable capacito, thee ae two sets of plates geneally mae of bass o aluminium. ii) One set of plates is static o fixe an is known as stato. iii) The othe set of plates which otates ove the stato by otating the pistons calle oto. iv) This capacito is geneally use in tuning cicuits in aio an T.V. eceives. 6 C C V Q

17 v) Symbol of vaiable Capacito is c) Multiple capacito: i) In a multiple capacito thee ae a numbe of paallel plates with mica sheets as a ielectic between them. ii) The capacitance is n times the capacitance between any two plates whee n numbe of mica sheets. iii) These ae use in high feuency oscillating cicuits as ielectic constant of mica oes not change with tempeatue. vi) These ae use as stana Capacitos in laboatoy. ) Pape capacito : i) In a pape capacito, pape soake in wax o oil acts as a ielectic. ii) Plates ae usually tin foils. It can be olle an seale in a cyline. iii) These ays to incease stability, pape is eplace by polystyene. vi) These occupy small space an cheape in cost. v) These ae use in aio cicuits an laboatoies e) Electolytic capacito : Tin foils Mica P P Tin foils Tin foils Pape soake in wax i) An electolytic capacito has two aluminium plates which ae place in a solution of ammonium boate. ii) When D.C. is passe though the capacito, vey thin film of aluminium oxie is fome on the anoe plate. iii) The thickness of the oxie laye is of the oe of 6 cm. electolyte A iv) Oxie laye acts as the ielectic between the plates. C v) This shoul be connecte to pope polaity in a cicuit oxie vi) In this capacito polaity of teminals will be inicate anoe A A vii) Wiely use when high capacitances ae euie. viii) Capacito of the oe of 3 μf ix) Can be obtaine with small volumes 39. Uses of conense (Capacito): a. Capacitos aea use to establish esie unifom an stong electic fiels in small space. b. Capacitos can confine stong electic fiel fo small volumes. They seve as useful evices fo stoing electical enegy. c. A capacito blocks iect cuent an allows altenating cuents. Capacitos ae use in filte cicuits.. Capacitos ae use in geneation an etection of oscillating electic fiels. e. Capacitos ae wiely use in tuning cicuits of aio an T.V. eceives. f. To euce voltage fluctuations in electic powe supplies, to tansmit pulse signals an to povie time elays capacitos ae essential. 7

18 4. Enegy of capacito : i) The electostatic enegy stoe in a chage capacito is eual to Q CV QV V o o. C ii) This enegy is stoe in the unifom electic fiel that is pesent between the plates of the capacito. 4. Combination of chage capacitos : i) If two conenses of capacities C an C ae chage to potentials V an V espectively an ae joine in paallel (ve plate connecte to ve plate), then the common potential Q Q CV CV V CV CV C C C C CV CV CC ii) The loss of enegy in this pocess (manifeste as heat) is given by U ( C C ( ) V V ). C V C V iii) When two conenses of capacities C an C chage to potentials V an V ae connecte antipaallel (ve plate connecte to ve plate) as shown in the figue. Q Q CV CV a) Common potential V C C C C C C b) Loss of enegy C V CV V C C C C ( C C ) ( V V ) c) Loss of enegy is moe in this case compae with pevious case. 4. Capacitance of spheical conense : a) Capacitance of single isolate sphee R whee R is its aius. b) In two concentic sphees (oute aius a an inne aius b). i) When the inne is chage an the oute is eathe, then C ε ab a b 4 Kab πε ( a b) ii) When the inne sphee is eathe, then ε a Ka C a b a b 43. Intouction of ielectic in a chage capacito A ielectic slab (K) is intouce between the plates of the capacito. S no Physical uantity With battey pemanently connecte With battey isconnecte. Capacity K time inceases K times inceases. Chage K times inceases Remains constant 3. P.D. Remains constant K times eceases 8

19 4. Electic Remains constant K times eceases 5. Intensity K times inceases K times eceases Enegy stoe in conense 44. The istance between the plates of conense is incease by n times. S n o. Physical uantity With battey pemanently connecte With battey isconnecte. Capacity n time eceases n times eceases. Chage n times eceases Remains constant 3. P.D. Remains constant n times inceases 4. Electic n time eceases Remain constant Intensity 5. Enegy n times eceases n times inceases stoe in conense 45. Combination of chage spheical ops : When n ientical chage small spheical ops ae combine to fom a Big op. Sno. Quantity Fo each chage small op Fo the big op a. Raius R n /3 b. Chage Q n c. Capacity C C n /3 C. Potential V V n /3 V e. Enegy ν ν n 5/3 ν f. Suface σ σ n /3. σ ensity of chage 46. ab-faa 9 faa, faa 9 stat-faa, coulomb 3x 9 stat-coulomb, 9

20 ab-coulomb coulomb, stat-volt 3 volt, volt 8 ab-volt. 47. Gauss Law : i) Statement : The total nomal electic flux φ e ove a close suface is times the total chage Q ε enclose within the suface. φ e Q ε ii) Gauss Law is applicable fo any istibution of chages an any type of close suface, but it is easy to solve the poblem of high symmety. iii) At any point ove the spheical Gaussian suface, net electic fiel is the vecto sum of electic fiels ue to, an. 48. Applications of Gauss Theoem: a) Electic fiel at a point ue to a line chage: A thin staight wie ove which amount of chage be unifomly istibute. l be the linea chage ensity i.e, chage pesent pe unit length of the wie. E π λ E π l This implies electic fiel at a point ue to a line chage is invesely popotional to the istance of the point fom the line chage. b) Electic fiel intensity at a point ue to a thin infinite chage sheet : amount of chage be unifomly istibute ove the sheet. Chage pesent pe unit suface aea of the sheet be σ.

21 E A E wheeσ A E is inepenent of the istance of the point fom the chage sheet. c) Electic fiel intensity at a point ue to a thick infinite chage sheet : amount of chage be unifomly istibute ove the sheet. Chage pesent pe unit suface aea of the sheet be σ. σ E A Electic fiel at a point ue to a thick chage sheet is twice that pouce by the thin chage sheet of same chage ensity. ) Electic intensity ue to two thin paallel chage sheets: Two chage sheets A an B having unifom chage ensities σ A an σ B espectively. In egion I : E ( σ A σ B) In egion II : E σ σ ( ) II A B In egion III : EIII ( σ A σ B ) e) Electic fiel ue to two oppositely chage paallel thin sheets : EI [ σ ( σ) ] σ E II [ σ ( σ) ] EIII ( σ σ )

22 f) Electic fiel ue to a chage Spheical shell amount of chage be unifomly istibute ove a spheical shell of aius R σ Suface chage ensity, σ 4π R i) When point P lies outsie the shell : E 4π This is the same expession as obtaine fo electic fiel at a point ue to a point chage. Hence a chage spheical shell behaves as a point chage concentate at the cente of it. σ.4πr E σ 4π 4π σ.r E ii) When point P lies on the shell : E σ iii) When Point P lies insie the shell: E The electic intensity at any point ue to a chage conucting soli sphee is same as that of a chage conucting speical shell. g) Electic Potential (V) ue to a spheical chage conucting shell (Hollow sphee) >, the electic potential, V 4 P lies on the suface( R), V R i) When point ( P3 ) lies outsie the sphee ( R) ii) When point ( ) P 3 R P P πε

23 <, V. R Note: The electic potential at any point insie the sphee is same an is eual to that on the suface. iii) When point ( P ) lies insie the suface ( R) Electostatics Note: The electic potential at any point ue to a chage conucting sphee is same as that of a chage conucting spheical shell. 3