Electrostatics PDF

CHAPTER ELECTROSTATICS ELECTRIC CHARGE Charge of a material body is that property due to which it interacts with other charges. There are two kinds of charges- positive and negative. S.I. unit is coulomb. Charge is quant...

CHAPTER ELECTROSTATICS ELECTRIC CHARGE Charge of a material body is that property due to which it interacts with other charges. There are two kinds of charges- positive and negative. S.I. unit is coulomb. Charge is quantized, conserved, and additive. COULOMB'S LAW r 1 q1 q 2 Force between two charges F = ˆr q1 q2 4p Î0 r 2 r If medium is present then multiply Î0 with Îr where Îr =relative permittivity NOTE :The Law is applicable only for static and point charges. Moving charges may result in magnetic interaction. And if charges are spread on bodies then induction may change the charge distribution. ELECTRIC FIELD OR ELECTRIC INTENSITY OR ELECTRIC FIELD STRENGTH (Vector Quantity) r r F It is the net force on unit positive charge due to all other charges. E = unit is N/C or V/m. q ELECTRIC FIELD DUE TO SPECIAL CHARGE DISTRIBUTION (c) Uniformly charged non conducting sphere: kq (a) Point charge E = r2 B C E ++ A Kq/R2 + ++ ++ P + + ++ + ++ R + r r ++ + E R ++ r q kq (i) EC = ; r>R r2 (b) Charged conducting sphere : kq (ii) EB = ; r=R R2 C E B kqr A (iii) EA = ; r R for point out side the sphere r r kq s (ii) E B = R2 = Î ; r=R for point at the surface of l sin ( ) = 2kl sin a+b the sphere 0 EP = 2p Î0 r 2 r ( ) a+b 2 (iii) EA = 0 ; r < R for point inside the sphere r 2kl For infinite line of charge : E P = ˆr r (e) Infinite charged conducting plate s æ x ö EP = ç1 - ÷ 2e0 è R2 + x2 ø E ++ ++++ + + r n^ P Null point for two charges : ++ + r + ++ r ++ Q1 Q2 If |Q1| > |Q2| Þ Null point near Q2 (Smaller charge) r s Q1 E= nˆ x= r (distance of null point from Q ) Î0 Q1 ± Q2 1 (f) Infinite sheet of charge (or charged non (+) for like charges; (–) for unlike charges conducting plate) r Equilibrium of suspended point charge ball system E ++ ++ ++ ^ s + + r nP ++ + r + ++ ++ l q q l Tcos q T q r s Q Q E= ˆ n Fe 2 Î0 Tsinq (g) Charged circular ring at an axial point : x mg ++ E + + + ++ + + r For equilibrium position Tcos q = mg & + + ++ Emax R E r O x P kQ2 Fe kQ2 R Tsin q =Fe= Þ tan q = = 2 x2 mg x2 mg ++ If whole set up is taken into an artificial satellite + + kQx kq 2 EP = ~ 0) T = Fe = (geff - 4l2 (R ) 2 3/2 + x2 2l R Field will be maximum at x = ± q q 2 180° At centre of ring x = 0 so E0 = 0 (h) Segment of ring : ELECTRIC FLUX r r l + f = ò E.dA + a 2kl æ aö r r + O E0 = sin ç ÷ è 2ø (i) For uniform electric field; f = E.A = EA cos R + R r l + where q = angle between E & area vector r ( A ). F lu x i s co ntr ib ut ed on ly d ue to t he (i) Due to charged disk co mpon e n t o f ele ct ri c f ie ld wh ich i s sC/m2 perpendicular to the plane. ++ r ++ + (ii) If E is not uniform throughout the area A , R ++ + r r ++ + then f = ò E.dA ++ + + E + ++ + x P r + +++ (iii) dA represent area vector normal to the surface +++ and pointing outwards from a closed surface. +  Gauss’s Law POTENTIAL DIFFERENCE r r The potential difference between two points A and åq Ñò E.ds = Î0 (Applicable only to closed surface) B is work done by external agent against electric field in taking a unit positive charge from B to A r r q without acceleration (or keeping Kinetic Energy f=Ñ ò E × d A = een0 (WBA )ext constant or Ki = Kf)) VA - VB =. q where qen= net charge enclosed by the closed surface. Electric potential f does not depend on the It is the work done against the field to take a unit (i) Shape and size of the closed surface positive charge from infinity (reference point) to the (ii) Th e ch ar ges locat ed o ut sid e th e clos ed given point without gaining any kinetic energy surface. (iii) Electric field depends on charges both inside é (W ) ù VP = ê ¥-P ext ú and outside the surface. ë q û w Electric field intensity at a point near a Potential Due to Special Charge Distribution s kq charged conductor : E = (i) Point charge V= Î0 r w Electrostatics pressure on a charged s2 V r conductor : P = 2 Î0 q p w Energy density in electric field: 1 (ii) Charged conducting sphere uE = Î E2 2 0 C V B ELECTRIC FIELD LINES Kq A R r R R A B kq kq (a) VC = ; r>R (b) VB = ; r=R qA>qB r R kq Electric lines of electrostatic field have following (c) VA = ; rR (b) VB = ;r=R strong field while distant lines weak field. r R (vii) Tangent to the line of force at a point in an kq éë3R2 - r 2 ùû electric field gives the direction of intensity of (c) VA = ; r