ELECTROSTATICS-PART 2A POWERPOINT PRESENTATIONBYBRAJESH KUMAR CHAUDHARYFACULTY OF PHYSICSRESONANCE EDUVENTURES PVT. LTD.NAGPUR, INDIA.
COULOMB’S LAWCHARLES COULOMB(1736-1806)The electric force between two charges is• proportional to the product of thecharges ,and•inversely proportional to the distancebetween them.
COULOMB’S LAWCoulomb used a torsion balance to investigateelectrostatic forces. A quantity of charge Q isrubbed on a fixed sphere B. A second chargeq is rubbed on a sphere A on the end of asuspended rod that is free to rotate. The forceexerted by Q on q twists the rod andsuspending fiber. Turning the suspension headtwists the fiber back so that the two spheresstay the same distance apart. The magnitude ofthe force is indicated by the angle throughwhich the suspension head is turned. Coulombfound that the force exerted by one charge onanother was directly proportional to themagnitudes of both charges (Q.q). He alsofound that force was inversely proportional tothe square of the distance, r, between thecharged spheres.
COULOMB’S LAW(Contd.)Force between the two particles ina medium1 221 12 2q qF F KrWhere,=force on particle 2 due to 1=force on particle 1 due to 1= distance between 1 & 2K = a constant of the medium21F12Fr
COULOMB’S LAW(Contd.)In vector form,1 221 2ˆq qF K rr1q2qrˆrWhere= unit vector in the increasing direction of rˆr
COULOMB’S LAW(Contd.)•Valid for point charges only• , where is permittivity of medium• = =permittivity of free space= relative permittivity of medium also known asdielectric constant of the medium= 1 for free space= for conductors14K0 r0rrr9 2 29 10 Nm C
COULOMB’S LAW(Contd.)•It is a conservative force.•It is a central force i.e., the force between the two particles isalways along the line joining the two particles.•Since it is central, hence in the absence of any external force,angular momentum of one particle with respect to the other (intwo particle system) is conserved.
PRINCIPLE OF SUPERPOSITION FORCOULOMB’S FORCEElectrostatic force is a two body interaction i.e. electrical force between twopoint charges is independent of presence or absence of other charges & so theprinciple of superposition is valid.THUS,Force on charged particles due to number of point charges is the resultant offorces due to individual point charges. Therefore, force on a point test chargedue to many charges is given by1 2 3 ...F F F F Q 1F2F3F
CONCEPT QUESTION #3+QA-QBA thin insulating rod is placed between two unlike pointcharges +Q & -Q. How will the forces acting on the chargeschange on insertion of rod?Source :Problem 3.1_ S.S. Krotov
NUMERICAL PROBLEM#2NaCl molecule is bound due toelectrical force between thesodium & the chlorine ionswhen one electron of sodiumis transferred to chlorine.Taking the separation betweenthe ions to be ,Find the force of attractionbetween them. State theassumptions (if any ) that youhave made.82.75 10 cmSource: Problem 13, Ch. 28_HCV
NUMERICAL PROBLEM #3A hydrogen atom consists of oneproton & one electron. It may beassumed that electron revolves in acircle of radius 0.53 angstrom. Withthe proton at its centre. Thehydrogen atom is said to be in groundstate in this case.Find(a)Magnitude of electric forcebetween the proton & theelectron.(b)Find the speed of the electron inthis case.Source: Problem 18,19, Ch. 28_HCV
NUMERICAL PROBLEM #3Two charged particles having charges 20 nC each areconnected by an insulating string of length 1m & thesystem is kept in a smooth horizontal table. Find thetension in the string.qqSource: Problem 21, Ch. 28_HCV
NUMERICAL PROBLEM #4Five point charges , each ofvalue q are placed on fivevertices of a regular hexagon ofside L. What is the magnitude ofthe force on a point charge ofvalue –q placed at the centre ofthe hexagon?Lq qqqq-q
NUMERICAL PROBLEM #5+q+q+q-2qThree equal point charges ofcharge +q each are movingalong a circle of radius R and apoint charge -2q is also placedat the centre of the circle asshown in the gig. If the chargesare revolving with constant andsame speed, then calculatespeed of charges.
NUMERICAL PROBLEM #6+Q +QTwo equally charged identical small metallic sphere A & B repeleach other with a force 20 μ N when placed in air(neglectgravitational attraction) . Another identical uncharged sphere C istouched to B & then placed at the mid point of the line joining A &B. What is the net electrostatic force on C?A B
NUMERICAL PROBLEM #7Source:Problem 3.3_I.E IrodovTwo small equally charged sphere, each of mass m, aresuspended from the same point by silk threads of length l.The distance between the spheres x<<l. find the rate dq/dtwith which the charge leaks off each sphere if theirapproach velocity varies as v= a/ √x , where a is a constant.
NUMERICAL PROBLEM #8A thin wire ring of radius r has an electric chargeQ. What will be the increment in the forcestretching the wire if a point charge q is placed atthe centre.qQSource:Problem 3.5_I.E Irodov
NUMERICAL PROBLEM #9Given a cube of side a with point charges q on each ofits vertices. Calculate the force exerted on any of thecharges due to rest of the 7 charges.qqqqqq q
NUMERICAL PROBLEM #10Two identical charged spheres are suspended by strings of equallength. The stings make an angle of 30 degrees with each other.When suspended in a liquid of density 0.8 gm/cc , the angleremain same. What is the dielectric constant of the liquid?Density of sphere = 1.6 gm/cc030 030In airIn liquid