Electrostatics Formulas and Concepts PDF

Electrostatics (Electric Field & Potenial) ELECTROSTATICS / FIELD Electrostatics is a branch of physics which deals with charge at rest charge is the origin of electromagnetic force. When charge is at rest then region around it calle...

Electrostatics (Electric Field & Potenial) ELECTROSTATICS / FIELD Electrostatics is a branch of physics which deals with charge at rest charge is the origin of electromagnetic force. When charge is at rest then region around it called electric field while the region around the moving charge called magnetic field. PROPERTIES OF CHARGE : 1. For a given closed system the total charge remains conserved. 2. Charge is always quantised i.e. Q = ±nc ; n  I Charge on any body is always in the integral multiple of one electronic charge (e = 1.6 × 10–19 coul). 3. Charge is relativistically invariant. TYPES MATERIAL There are three kinds of material on the basis of conductivity. (a) Conductor : Having large number of mobile electrons. It is approximately 1021 electrons/c.c. (b) Bad conductor : Having very small number of free electrons, it is approximately 107 electrons c.c (c) Semi conductor : Conductivity lies between conductor and insulator. Number of free electrons is approximately 104 electron/c.c. COULOMB’S LAW : When two point charges q1 and q2 are separated by a distance r then force of mutual intraction F is given by F  q1q 2 when r = constant. 1 and F when q1q2 = constant r2 q1q 2 qq Hence F 2 or F  k. 1 2 2 ; K is proportionality constant r r 1 q1q 2 1 9 In SI units, F. 0  8.85  1012 Fm and 4   9  10 nt m coul 2 –2 4 0 r 2 ; 0 q1q 2 In cgs units, F ; 0 is per mittivity of the vacuum. r2 When there is a medium in the intervining region of two charges then 1 qq F. 1 2 2 ( Îr is the relative permitivity of medium) 4 0 r r Îr is the relative permitivity which is the dimensionless qunatity that gives the factor by which force is reduced compared to vaccum.  Electrostatics F0 r  Fm , F0 is the force in vacuum and Fm is force in medium. 0 r  Absolute permittivity of the medium. q1 uuur A r 1 q1q 2 BA FAB .. uuur r1 q2 4 0 | BA |2 | BA | B r2 r uuur O q1q 2 FAB  uuur 3. BA 4 0 | BA | uuur uuur uuur ur ur where BA  OA  OB  r1  r2 r q1q 2 ur ur FAB  ur ur 3. (r1  r2 ) 4 0 | r1  r2 | when q1q2 > 0, Force is attractive and q1q2 < 0, Force is repulsive PROCESS OF CHARGING : (1) By rubbing or friction - when two bodies are rubbed together there is transfer of electrons from body, which is surplus in electron to another body which is surplus in electrons and get positive charge of equal amount to negative charge. (2) By conduction - when a charged body is in contact with another uncharged one threre is redistribution of charges on entire are is of both bodies followed by mechanical separation. The amount of charge redistribution on body depends on surface area. (3) By induction - when an uncharged body is brought near charged on the charge opposite nature induced over the uncharged one. The induced charge is always less than or equal to inducing charge. Induction is always followed by attraction, but attraction is not the surest test of induction. If q be inducing charge, then charge induced on a body having dielectric constant K is given by  1 q '  q 1   , if charge is induced on the surface of a conductor then induced charge is  K q '  q (As k is infinity for a conductor) DISTRIBUTION OF CHARGES : (a) Linear charge distribution : - If charge gets appeared on a body of linear dimension. Linear charge density ( )  charge per unit length. (b) Surface charge distrbution :- If charge gets appeared on a body having two dimensions. Surface charge density ( ) = charge per unit area (c) Volume charge density : If charge is enclosed in a volume; Volume charge density=charge per unit volume Electric field : The site around the charge at rest called electric field. Electric field strength or Electric intensity is defined as the force experienced by a unit positive charge. r F E  lim where q0 is the positive test charge. q0 0 q 0 Electrostatics r 3 1 Unit of E is newton coulmob and dimension is  MLT A . The resultant electric field at any point is r r r r equal to vector sum of electric field at that point due to various charges i.e. E  E1  E 2  E3 ..... Resultant of two electric fields which are at an angle θ is given by E 2 sin  E  E12  E 22  2E1E 2 cos and tan   E1  E 2 cos  r r  is the angle of E with E1 r Electric field intensity (E) for some body having uniformly continuous charge distribution. 1. Electric field strength due to a point charge at a distance r is given by r 1 q E1 . rˆ 4 0 r 2 2. Electric field strength due to a uniformly charged ring at a distance x from centre of the axis of ring.. + q + + + + r 1 qx + R + E + + 4 0 (x 2  R 2 )3/ 2 + O x P + + + + R ur E becomes max at x  : Direction of E is away from centre along axis. 2 3. Electric field strength due to uniformally charged rod of length l at a distance r along perpendicular line from centre and linear charge density is . q E l2 4 0 r  r2 4 where  = charge per unit length when l   E 2 0 r 4. Electric field strength due to uniformally charged spherical shell of radius R at a distance r from, centre of shell E = 0, if r