Title X_OLY._PHY._(ELE.STA.).pdf ✅

Olympiad Text Book X-Physics (Vol-1) Narayana Group of Schools 1 ELECTROSTATICS ELECTROSTATICS_SYNOPSIS-1 ELECTROSTATICS :The study of electrical effects of charge at rest is called “electrostatics”. 1. CHARGE a) Charge is the fundamental property associated with matter due to which it produces and experiences magnetic and electric effects. b) The deficiency of electrons on the body is known as positive charge. The excess of electrons on a body is known as negative charge. c) Just as masses are responsible for the gravitational force, charges are responsible for electric force. d) The net charge of a neutral body is zero and it is equal to sum of positive and negative charges on it. 2. PROPERTIES OF CHARGES a) Like charges repel each other and unlike charges attract each other. b) Electric charge is additive in nature. i.e., the total charge on a body is algebric sum of the charges located at different points on the body. c) The charge is always quantised i.e., electric charge can exist only as an integral multiple of charge of an electron. i.e., if q is the charge then q ne   . Where n is an integer. d) The total net charge of an isolated physical system always remains constant. Charge can neither be created nor destroyed but it can be transferred from one body to another. (Law of conservation of charge). e) A charged body attracts an other uncharged light particles. f) Charge always resides on the outer surface of the charged body. It accumulates more at sharp points. g) Charge is a scalar. SI unit of charge is coulomb. Charge is a derived physical quantity with dimensions [AT] h) Charge can not exist without mass through mass can exist without charge. Eg: Particles like photon, neutrino have no rest mass so they can never have a charge i) Charge is independent of frame of reference. i.e., charge on a body does not change what ever be its speed. (charge is invariant). j) Accelerated charge radiates energy. If the motion of a charged particle is accelerated it not only produces electric and magnetic fields but also radiates energy in the form of electromagnetic waves. k) Charge of e–1 = –1.6×10–19 C, Charge of proton p+ = 1.6×10–19 C, Mass of electron = 9.1 × 10–31 kg, Mass of proton = 1.67 × 10–27 kg, Mass of neutron = 1.67 × 10–27 kg. 3. ELECTRIFICATION a) A body can be charged by friction, conduction or induction.
X-Physics (Vol-1) Olympiad Text Book Narayana Group of Schools 2 b) Friction: When two bodies are rubbed together, electrons are transferred from one body to the other. The substance which loses the electrons is said to have acquired positive charge and the substance which gains electrons is said to have acquired negative charge. Here both positive and negative charges are in equal amounts. Eg: When a glass rod is rubbed with silk cloth, glass rod acquires positive charge and silk cloth acquires negative charge. When an ebonite rod is rubbed with fur, ebonite rod acquires negative charge and fur cloth acquires positive charge. c) Conduction: If a neutral body is kept in contact with a charged body, the latter shares its charge with the former. Conduction preceeds repulsion. d) Induction: If a charged body is brought near a neutral body, the charged body will attract opposite charge and repel similar charge present in the neutral body. Opposite charge is induced at the near end and similar charge at the farther end. Inducing body neither gains nor loses charge. Induction always preceeds attraction. Note: i) Repulsion is the sure test of electrification. Coulomb’s Law – Forces Between two point Electric charges Coulomb’s law : The electrostatic force of interaction between two point electric charges is directly proportional to the product of the charges, inversely proportional to the square of the distance between them and acts along the straight line joining the two charges. Strictly speaking, Coulomb’s law applies to stationary point charges. Mathematical expression : Consider two point charges q1 and q2 separated by a distance r. Let F be the electrostatic force between these two charges. q1 r q2 According to Coulomb’s law, i) F q q  1 2 ii) 2 1 F r  Combining (i)and (ii) , 1 2 2 q q F r   1 2 2 q q F k r  Where k is a positive constant of proportionality called electrostatic force constant or Coulomb constant. Its value depends upon the system of units and also on the medium between the two charges. In SI, 0 1 1 k 4 4 K        0K 1 2 2 0 1 q q F 4 K r  
Olympiad Text Book X-Physics (Vol-1) 3  is absolute electrical permittivity of the dielectric medium between the charges, 0  is the permittivity of free space i.e., vacuum. The ratio 0   is denoted by K (or) r  . It is known as dielectric constant or dielectric coefficient or relative permittivity or specific inductive capacity of the medium between the charges. If the two point charges are located in Vacuum, then K = 1, 0    and 0 1 , 4 k    In this case, 1 2 2 0 1 q q F 4 r   The permittivity of free space, 0  , as determined by experiment is 8.8542 × 10-12 C2N-1m-2 . The approximate value may be taken as 9 × 10-12 C2N-1m-2 . The value of 0 1 4 is 8.9875 x 109 Nm2C-2. For the sake of mathematical convenience, the value of 0 1 4 is taken as 9 x 109 Nm2C-2 . In CGS system, the value of 0 1 4 is 1.  1 k , K  Dimensional formula of        1 2    1 3 4 2 0 2 2 2                       q q AT AT M L T A F r MLT L  Units of Charge: In SI, the unit of charge is coulomb (C). One Coulomb of charge is that charge which when placed at rest in vacuum at a distance of one metre from an equal and similar stationary charge repels it and is repelled by it with a force of 9 x 109 newton. Relative Permittivity or Dielectric Constant : i) The relative permittivity or the dielectric constant ( r  or K) of a medium is the ratio of the absolute permittivity  of the medium to the permittivity 0  of free space. 0 r     ii) Relative permittivity in terms of forces between electric charges. If two charges q1 and q2 are separated by distance r in vacuum, then the magnitude of force between them is given by 1 2 2 0 1 4 q q F r    .........(1)
X-Physics (Vol-1) Olympiad Text Book 4 If the same charges are separated by the same distance in a medium of relative permittivity r  , then the magnitude of force between the charges is given by 1 2 2 0 1 4 m r q q F   r  ............... (2) Dividing (1) and (2), We get r m F F    -—————(3) This leads us to the following definition of dielectric constant. Dielectric constant or relative permittivity of a medium is the ratio of the electrostatic force between two charges separated by a certain distance in vacuum to the electrostatic force between the same two charges separated by the same distance in that medium. If follows from equation (3) that m r F F    We can conclude from here that the presence of a dielectric reduces the force between two charges. Clearly, the two charges exert maximum force on each other when they are placed in vacuum.  In a cold dry day, metallic surfaces become highly charged. Why ? Reason : In normal days the atmosphere gets ionized due to friction. But water carries this charge around. However on a cold dry day, the air gets ionized and since there is no humidity it remains in the air. This charge induces charge in the metal. Every day in life Coulomb’s Law in vector form: Consider two point charges q1 and q2 separated by a distance r. If q1 q2 > 0 i.e., if both q1 and q2 are +ve or both q1 and q2 are negative, then the charges repel each other as shown in Fig. on the other hand, if q1 q2 < 0 i.e., if the charges are dissimilar, then the charges attract each other as shown in fig. r q1 q2 F12 r12 r21 F21 If F21  is the force exerted on charge q2 by charge q1 and q1 q2 > 0,then 1 2 21 12 2 0 1 4 q q F r  r    ..........(1) Where r12  is a unit vector pointing from q1 to q2 .