Title 1. ELECTROSTATICS.pdf ✅

Charge is the property associated with matter due to which it produces and experiences electrical and magnetic effects. All bodies consist of atoms, which contain equal amount of positive and negative charges in the form of protons and electrons respectively. The number of electrons being equal to the number of protons as an atom is electrically neutral. If the electrons are removed from a body, it gets positively charged. If the electrons are transferred to a body, it gets negatively charged. “Similar charges (charges of the same sign) repel one another; and dissimilar charges (charges of opposite sign) attract one another.” 1.1 WAYS OF CHARGING A BODY (i) Charging by friction When two bodies are rubbed together, a transfer of electrons takes place from one body to another. The body from which electrons have been transferred is left with an excess of positive charge, so it gets positively charged. The body which receives the electrons becomes negatively charged. “The positive and negative charges produced by rubbing are always equal in magnitude.” When a glass rod is rubbed with silk, it loses its electrons and gets a positive charge, while the piece of silk acquires equal negative charges. An ebonite rod acquires a negative charge, if it is rubbed with wool (or fur). The piece of wool (or fur) acquires an equal positive charge. (ii) Charging by electrostatic induction If a positively charged rod is brought near an insulated conductor, the negative charges (electrons) in the conductor will be attracted towards the rod. As a result, there will be an excess of negative charge at the end of the conductor near the rod and the excess of positive charge at the far end. This is known as ‘electrostatic induction’. The charges thus induced are found to be equal and opposite to each other. Now if we touch the far end with a conductor connected to the earth, the positive charges here will be cancelled by negative charges coming from the earth through the conducting wire. Now, if we remove the wire first and then the rod, the induced negative charges which were held at the outer end will spread over the entire conductor. It means that the conductor has become negatively charged by induction. In the same way one can induce a positive charge on a conductor by bringing a negative charged rod near it. ELECTROSTATICS 1 ELECTRIC CHARGE PHYSICS BOOKLET FOR JEE NEET & BOARDS
Insulated + + + + + + +     + + + + + + + + + +     + + + + + + + + +       +     + + + + + + + + +               Important points regarding electrostatic induction (a) Inducing body neither gains nor loses charges. (b) The nature of induced charge is always opposite to that of inducing charge. (c) Induced charge can be lesser or equal to inducing charge but it is never greater than the inducing charge. (d) Induction takes place only in bodies (either conducting or nor conducting) and not in particles. (iii) Charging by conduction Let us consider two conductors, one charged and the other uncharged. We bring the conductors in contact with each other. The charge (whether negative or positive) under its own repulsion will spread over both the conductors. Thus the conductors will be charged with the same sign. This is called ‘charging by conduction (through contact)’. 1.2 UNIT OF CHARGE In SI units as current is assumed to be fundamental quantity and        t q I , charge is a derived physical quantity with dimensions [AT] and unit (ampere  second) called ‘coulomb (C)’. The coulomb is related to CGS units of charge through the basic relation 1 coulomb = 3  109 esu of charge = 10 1 emu of charge 1.3 PROPERTIES OF CHARGE (i) Charge is always associated with mass The charge can not exist without mass though mass can exist without charge. (ii) Charge is quantised When a physical quantity can have only discrete values rather than any value, the quantity is said to be quantised. Several experiments have established that the smallest charge that can exist in nature is the charge of an electron. If the charge of an election (= 1.6  1019C) is taken as the elementary unit, i.e., quanta of charge, and is denoted by e, the charge on any body will be some integral multiple of e, i.e., q = ne ; n = 1, 2, 3, ........... ... (1)
charge on a body can never be       3 2e , (17.2) e or (105 ) e etc. (iii) Charge is conserved A large number of experiments show that in an isolated system, total charge does not change with time, though individual charges may change, i.e., charge can neither be created nor be destroyed. This is known as the principle of conservation of charge. (iv) Charge is invariant This means that charge is independent of frame of reference, i.e., charge on a body does not change whatever be its speed. 1.4 CONDUCTORS AND INSULATORS The conductors are materials, which allow electricity (electric charge) to pass through them due to the presence of free elections. e.g., metals are good conductors. The insulators are materials, which do not allow electric charge to pass through them as there is no free electrons in them. e.g. wood, plastics, glass etc. Illustration 1 Question: How many electrons must be removed from a piece of metal so as to leave it with a positive charge of 3.2  1017 coulomb? Solution: From ‘Quantization of charge’, we know Q = ne n = C C e Q 19 17 6.1 10 2.3 10      = 200 Illustration 2 Question: A copper penny has a mass of 32 g. Being electrically neutral, it contains equal amounts of positive and negative charges. What is the magnitude of these charges inC. A copper atom has a positive nuclear charge of 3  1026 C. Atomic weight of copper is 64g/mole and Avogadro’s number is 6  10 –26 atoms/mole. Solution: 1 mole i.e., 64 g of copper has 6  1023 atoms. Therefore, the number of atoms in copper penny of 32 g is   3 23 1032 64 6 10 – 3 × 1020 One atom of copper has each positive and negative charge of 3  1026 C. So each charge on the penny is (3  1020)  (3  10 –26) = 9C. “Two stationary point charges repel or attract each-other with a force which is directly proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them.” A r B q1 q2 Let ‘r’ be the distance between two point charges q1 and q2. According to Coulomb’s law, we have F 2 21 |||| r qq  where F is the magnitude of the mutual force that acts on each of the two charges q1 and q2. 2 COULOMB’S LAW
or, F = 2 21 ||| r qqK , where K is a constant of proportionality The value of K depends upon the medium in which two point charges are placed. In the SI system. K = 4 0 1  for vacuum (or air) The constant 0 ( = 8.85 × 10–12 C2 /N-m2 ) is called “permittivity” of the free space. Thus F = 2 21 0 | || | 4 1 r qq   9 × 109 2 21 | || | r qq ... (2) 2.1 PERMITTIVITY OF A MEDIUM If the medium between the two point charges q1 and q2 is not a vacuum ( or air). Then the electrostatic force between the two charges becomes F = 4 1 2 21 |||| r qq = r   4 0 1 2 21 |||| r qq ... (3) where  = 0r is called the ‘absolute permittivity’ or ‘permittivity’ of the medium and r is a dimensionless constant called ‘relative permittivity’ of the medium which is a constant for a given medium. r is also sometimes called “dielectric constant’ or ‘specific inductive capacity’ of the medium. 2.2 COLOUMB’S LAW IN VECTOR FORM The vector form of Coulomb’s law is 2 21 r Kq q F   rˆ ... (4) The unit vector rˆ has its origin at the ‘source of the force”. For example, to find the force on q2, the origin of rˆ is at q1. The signs of the charges must be explicitly included in equation (4). If F is the magnitude of the force, then  F = + rF ˆ means a repulsion, whereas  rFF ˆ  means an attraction. r q1 q2 rˆ  F According to the principle of superposition, the force acting on one charge due to another is independent of the presence of charges. So, we can calculate the force separately for each pair of charges and then take their vector sum or find the net force on any charge. The figure shows a charge q1 interacting with other charges. Thus, to find the force on q1, we first calculate the forces exerted by each of the other charges, one at a time. The net force 1  F on q1 is simply the vector sum 1 141312   FFFF + ... (5) – + – + 14  F q2 q3 q4 12  F q1 13  F where 12  F is the force on the charge q1 due to the charge q2 and so on. PRINCIPLE OF SUPERPOSITION 3