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7 ELECTROSTATICS 01
Chapter 01 Electrostatics 1. Electric Charge 1.1 Definition Charge is the property associated with matter due to which it produces and experiences electrical and magnetic effects. 1.2 Type There exists two types of charges in nature (i) Positive charge (ii) Negative charge Charges with the same electrical sign repel each other, and charges with opposite electrical sign attract each other. 1.3 Unit and dimensional formula S.I. unit of charge is coulomb (C), ( ) 3 6 9 1mC 10 C, 1 C 10 C, 1nC 10 C − − − =  = = C.G.S. unit of charge is e.s.u. 1C = 3 × 109 e.s.u. Dimensional formula [Q] = [AT]. 1.4 Point Charge Whose spatial size is negligible as compared to other distances. 1.5 Properties of charge (i) Charge is a Scalar Quantity: Charges can be added or subtracted algebraically. (ii) Charge is transferable: If a charged body is put in contact with an uncharged body, uncharged body becomes charged due to transfer of electrons from one body to the other. (iii) Charge is always associated with mass, i.e., charge can not exist without mass though mass can exist without charge. (iv) Charge is conserved: Charge can neither be created nor be destroyed. (v) Invariance of charge: The numerical value of an elementary charge is independent of velocity. (vi) Charge produces electric field and magnetic field: A charged particle at rest produces only electric field in the space surrounding it. However, if the charged particle is in non accelerated motion it produces both electric and magnetic fields. And if the motion of charged particle is accelerated it not only produces electric and magnetic fields but also radiates energy in the space surrounding the charge in the form of electromagnetic waves. (vii) Charge resides on the surface of conductor: Charge resides on the outer surface of a conductor because like charges repel and try to get as far away as possible from one another and stay at the farthest distance from each other which is outer surface of the conductor. This is why a solid and hollow conducting sphere of same outer radius will hold maximum equal charge and a soap bubble expands on charging. (viii) Quantization of charge: When a physical quantity can have only discrete values rather than any value, the quantity is said to be quantized. The smallest charge that can exist in nature is the charge of an electron. If the charge of an electron ( ) 19 "e" 1.6 10 C − = −  is taken as elementary unit i.e. quanta of charge the charge on any body will be some integral multiple of e i.e., Q = ± ne with n = 0, 1, 2, 3 ...... Charge on a body can never be 0.5 e, ±17.2 e or ±10–5 e etc. 1.6 Comparison of Charge and Mass We are familiar with role of mass in gravitation, and we have just studied some features of electric charge. We can compare the two as shown below: Charge Mass 1. Electric charge can be positive, negative or zero. 1. Mass of a body is a positive quantity. 2. Charge carried by a body does not 2. Mass of a body increases with its velocity as Fig 1.1: Types of Charges SCAN CODE Electrostatics
depend upon velocity of the body 0 2 2 m m 1 / c = −  where c is velocity of light in vacuum, m is the mass of the velocity  and m0 is rest mass of the body. 3. Charge is quantized. 3. The quantization of mass is yet to be established. 4. Electric charge is always conserved. 4. Mass is not conserved as mass can be converted into energy 5. Force between charges can be attractive or repulsive 5. The gravitational force between two masses is always attractive. 1.7 Methods of Charging A body can be charged by following methods: (i) By friction: In friction when two bodies are rubbed together, electrons are transferred from one body to the other. As a result of this one body becomes positively charged while the other negatively charged, e.g., when a glass rod is rubbed with silk, the rod becomes positively charged while the silk becomes negatively charged. However, ebonite on rubbing with wool becomes negatively charged making the wool positively charged. Clouds also become charged by friction. In charging by friction in accordance with conservation of charge, both positive and negative charges in equal amounts appear simultaneously due to transfer of electrons from one body to the other. (ii) By electrostatic induction: If a charged body is brought near an uncharged body, the charged body will attract opposite charge and repel similar charge present in the uncharged body. As a result of this one side of neutral body (closer to charged body) becomes oppositely charged while the other is similarly charged. This process is called electrostatic induction. NOTE: Inducting body neither gains nor loses charge. (iii) Charging by conduction: Charging by conduction involves the contact of a charged object to a neutral object. Hence when an uncharged conductor is brought in contact with a charged conductor, charge is shared between the two conductors and hence the uncharged conductor gets charged. NOTE: Inducting body neither gains nor loses charge. A truck carrying explosives has a metal chain touching the ground, to conduct away the charge produced by friction. Fig 1.2 Fig 1.3 SCAN CODE Electrostatics ELECTROSTATICS 9
It is a simple apparatus with which the presence of electric charge on a body is detected. When metal knob is touched with a charged body, some charge is transferred to the gold leaves, which then diverges due to repulsion. The separation gives a rough idea of the amount of charge on the body. If a charged body is brought near a charged electroscope the leaves will also diverge as the charge on body is similar to that on electroscope and will usually converge if opposite. If the induction effect is strong enough, leaves after converging may again diverge. In case of uncharged electroscope, if the charged body is brought is contact, the electroscope gets charged and the leaves diverge. when a charged body is brought near electroscope (but not is contact), different charges appear on different parts of electroscope resulting in divergence of leaves. (1) Uncharged electroscope (2) Charged electroscope 1 2 2 q q F k r = where k is a proportionality constant. In SI units k has the value, k = 8.988 × 109 N m2 /C2 9.0 × 109 N m2 /C2 (a) The direction of force is always along the line joining the two charges. (b) The force is repulsive if the charges have the same sign and attractive if their signs are opposite. (c) This force is conservative in nature. (d) This is also called inverse square law. 2.1 Variation of k Constant k depends upon system of units and medium between the two charges. 2.1.1 Effect of units (a) In C.G.S. for air k = 1, 1 2 2 kQ Q F r = Dyne (b) In S.I. for air 2 9 2 0 1 N m k 9 10 , 4 C − = =   1 2 2 0 1 Q Q F . 4 r =  Newton (1 Newton = 105 Dyne) NOTE: • Absolute permittivity of air or free space = 2 12 2 C Farad 8.85 10 . N m m −    =  −   Dimension is 1 3 4 2 M L T A − −     • 0 relates with absolute magnetic permeability (0) and velocity of light (c) according to the following relation 0 0 1 c =   2.1.2 Effect of medium (a) When a dielectric medium is completely filled in between charges rearrangement of the charges inside the Fig 1.4 Fig 1.5 2. Coulomb’s Law If two stationary and point charges q1 and q2 are kept at a distance r, then it is found that force of attraction or repulsion between them is proportional to the product of the two charges and inversely proportional to the square of the distance between them. Mathematically, Coulomb’s law can be written as 1.8 Electroscope Fig 1.6 SCAN CODE Electrostatics ELECTROSTATICS 10