ELECTROSTATICS. 4πε0. E dr. The electric field is along the direction where the potential decreases at the maximum rate. 5. Electric Potential Energy:

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1 LCTROSTATICS. Quntiztion of Chge: Any chged body, big o smll, hs totl chge which is n integl multile of e, i.e. = ± ne, whee n is n intege hving vlues,, etc, e is the chge of electon which is eul to.6 9 C.. Coulomb s lw: F = ˆ F. lectic Field: =, whee is the unit ositive chge. φ lectic field is lso eul to lectic flu (φ) e unit noml e. =. A Field due to oint chge: = 4. lectic Potentil: lectic otentil due to numbe of oint chges Potentil Diffeence: dv V V = d = d n i V = i= i The electic field is long the diection whee the otentil deceses t the mimum te. 5. lectic Potentil negy: lectic otentil enegy between two oint chges U = 6. lectic Diole Moment: Two oint chges of eul mgnitude but oosite signs seted by smll distnce fom n electic diole. Diole moment is vecto untity, = l. e l α b Diection of diole is fom to. Potentil t the oint P: cos V = dv = = cos t d dv = sin d = = cos tn α = tn

2 This eution gives the electic field t ny oint P t distnce fom the diole. Toue on Diole in n lectic field: Toue = lsin In vecto fom: Toue = Potentil negy of Diole in n lectic Field: U = No electic field cn eist inside conducting mteil. Foce on diole: F = whee is the deivtive of electic field with esect to distnce long the diection of the diole. Guss Theoem: da =, whee is eul to the net chge enclosed with the sufce. Guss lw fo Gvittion: g da = 4πGM, whee M is the totl mss enclosed within the closed sufce. 7. Ccitnce: Ccito is device fo stoing chge. Mthemticlly, Q = CV, the unit of C in fd. Fo llel lte ccito: C = A, whee A = Plte e, d = Distnce between the ltes d Q 8. negy Stoed in Ccito: U = = CV = QV C U 9. negy Stoed e Unit Volume in n lectic Field (): = Volume. lectosttic Pessue: P =, whee is sufce chge density.. lectic field nd otentil fo tyicl situtions: S.No. System lectic field intensity Potentil. Isolted chge. l Diole y Isolted chge, y >> P. V 4 = = 4 π π =. 4 π =. 4 π y V = π 4 V = cos cos = V =

3 . A ing of chge R 4. A disc of chge R 5. Infinite sheet of chge. V = R = / 4 π (R ) = R whee is sufce chge density. V = [ R ] = Infinitely long line of chge = whee is line chge density Finite line of chge β α P 8. Chged sheicl shell 9. Solid shee of chge R = (sinα sin β) = (cosα cos β) ) Inside, R, = b) Outside, R, = ρ ) Inside, R, = b) Outside, R, = ρ R R ρ volume chge density. sec tn V = ln β β 4 π sec α tn α ) Inside, R,V= R b) Outside, R, V= ) Inside, ρr R, V= 6 R b) Outside, ρr R, V = Note: With oe modifictions the bove fomule cn be lied in Gvittion lso. (Like M, G). Potentil t the edge of disc V = R. π R Sel enegy of chged conducting shell: U = 8 π R Self enegy of the unifomly chged shee (non-conducto): U = π R 5. Aliction of Guss s Lw in the Region of vying electic field:

4 Conside the sitution s shown in figue. In egion electic field deends on diection s =. Findthe net chge enclosed in the cube. y φ in = In the cube of edge shown in figue fom font fce electic flu goes in 4 in which cn be given s φ = () = 4 O φ out Fom the othe sufce flu coming out cn be given s 4 out () 9 φ = =. Hee φ out > φin fo the cubicl sufce hence net chge enclosed in the cube is ositive, we cn ly Guss Lw to find the net chge enclosed in the cube s encl 4 φ φ = o = 5. out in encl Pevious uestions:. A few electic field lines fo system of two chges Q nd Q fied t two diffeent oints on the -is e shown in the figue. These lines suggest tht () ) Q > Q b) Q < Q c) t finite distnce to the left of Q the electic field is zeo d) t finite distnce to the ight of Q the electic field is zeo Sol. (, d) Numbe of electic field lines oiginting fom Q is moe thn teminting t Q. Q > Q Hee, Q is ositive while Q is negtive. Since Q > Q, theefoe electic field will be zeo t finite distnce to the ight of Q.. A unifomly chged thin sheicl shell of dius R cies unifom sufce chge density of e unit e. It is mde of two hemisheicl shells, held togethe by essing them with foce F (see figue). F is ootionl to () F F ) R b) R c) R Sol. (). A sheicl otion hs been emoved fom solid shee hving chge distibuted unifomly in its volume s shown in the figue. The electic field inside the emtied sce is ) zeo eveywhee *b) non-zeo nd unifom c) non-unifom d) zeo only t its cente 4. Thee concentic metllic sheicl shells of dii R, R, R, e given chges Q, Q, Q esectively. It is found tht the sufce chge densities e sme given to the shells, Q : Q : Q is ) : : *b) : : 5 c) : 4 : 9 d) : 8 : 8 d) R Pssge: A non-unifom, but sheiclly symmetic, distibution of chge hs chge density ρ() given s follows :

5 4 ρ () = ρ fo R R ρ () = fo R whee ρ is ositive constnt. 5. The totl chge contined in the chge distibution is 4 ) ρ π R b) ρπr c) R π ρ *d) zeo 6. The ntue of the gh between electic field s function of is *) b) c) d) 7. The mimum electic field is ρr ρr ) b) 6 ρr c) ρr *d)