## Electrostatics

Introduction:$\\$The study of charges at rest is called static electricity or electrostatics.$\\$Charges are produced due to actual transfer of electrons.$\\$Positive charge means the deficiency of electrons while negative charge means excess (gain) of electrons.$\\$So, during charge transfer there is change in mass too. Thus, mass of -vely charged body is greater than that of -vely charged body.$\\$The attraction and repulsion of two charged objects are sometimes summarized as “Like charges repel, and opposite charges attract.” But keep in mind that the phrase “like charges” does not mean that the two charges are exactly identical, only that both charges have the same algebraic sign (both positive or both negative). “Opposite charges” means that both objects have an electric charge, and those charges have different signs (one positive and the other negative).

## Properties of charges:

1. Quantization of charge$\\$Electric charge can exist only as an integral multiple of charge on an electron (-e) i.e.$\\$q= +ne, where ‘n' is an integer. The possible values of electric charges are$\\$q=±1e,±2e,±3e,…………$\\$Charge less than the charge on an electron (i.e. e=1.6×*$10^{-19}$ C ) is not possible.$\\$

2. Conservation of charge$\\$(a) On an isolated system, total electric charge always remains constant.$\\$(b) Total charge on a body is equal to algebraic of all the charges present on it. Every atom is electrically neutral as it contains as many electrons as the number of protons in it.$\\ \\$When we rub a glass rod with a piece of silk, the +ve charge acquired by the glass rod is equal to -ve charge acquired by silk piece. Thus charges are produced in equal and unlike pairs.$\\$Like charges repel each other while unlike charges attract each other. Repulsion is sure test of electrification. A charged body may attract a neutral body or an oppositely charged body but it always repels a similarly charged body.$\\$The magnitude of charge is not affected by its motion like mass i.e. charge is invariant. At very high speed (v=c), it is found that mass of a particle becomes m=$\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}} \\$Where $m_0$ is the rest mass of particle.$\\$A charge at rest produces only electric field around itself, A charge having unaccelerated (uniform) motion produces$\\$electric as well as magnetic field around it. While a charge having accelerated motion emits electromagnetic radiation also in addition to producing electric and magnetic fields.

## Mode of Charging:

1. Friction$\\$In this method body is charged by rubbing one surface with another and charge is induced .$\\$It is due to the transfer of electron from one body another by the thermal effect.$\\$

2. Induction$\\$

3. Conduction → By contact$\\$Charging a body by induction is preferable since the same charged body can be used to charge any$\\$number of bodies without loss of charge.$\\$

If q is the inducing charge, then charge induced on a body having dielectric constant $ε_r$ is given by $q_{induced} = q_{inducing} (1-\frac{1}{ε_r}$)$\\$where $ε_r$ is dielectric constant of uncharged body.$\\$-ve sign represents opposite nature of$\\$induction. For air or vacuum, $ε_r$ or K=1$\\$for conductor, $ε_r$ = $\\$for insulator $ε_r$>1$\\$Case I: When uncharged body is conductor.$\\$K=$\\$$q_{induced} = q_{inducing} (1-\frac{1}{∞}) \\$Thus for conductor $q_{induced} = q_{inducing} \\$Case II: When uncharged body is insulator$\\$i.e. K>1$\\$•Thus, q induced < $q_{inducing}$$\\$Case III: For air$\\$K or $ε_r$=1$\\$$q_{induced}$=0$\\$So, there is no induction in air.$\\$###Conclusion:$\\$$q_{induced}≤q_{inducing}$$\\$In induction process, net induced charge on a body will be zero. In induction process,$\\$both charge and mass of charge body remain same but potential of charging body decreases.$\\$

4. Types of charge carriers:$\\$Substances are classified into 3 categories on the basis of flow of charge or electricity through them.$\\$Conductors: These easily allow electricity to pass through them.$\\$E.g.:-Metals, Earth, human body, etc.$\\$Insulators: These do not allow electricity to pass through them.$\\$E.g.:- Wood, Mica, glass, paper, etc.$\\$

Semiconductors: These lie in between conductors and insulators in their ability to conduct electricity.$\\$

E.g.:- Silicon and Germanium.$\\$

5. Charge Density:$\\$Linear charge density(𝛌)$\\$Charge per unit length on linear object called linear charge density and denoted by λ.$\\$Its unit is coulomb per meter (C$m^{-1}$ )$\\$$λ=\frac{q}{l} \\$**Surface charge density (σ) **$\\$Charge per unit area is known as surface charge density.$\\$Its unit is coulomb per$\\$square meter (C$m^{-2}$ ) i.e.$\\$$σ=\frac{q}{A} \\$Surface charge density on a charged conductor decreases with increase of radius of curvature and vice-versa.$\\$It is highest at the sharpest point of a conductor.$\\$Volume charge density ( ρ)$\\$Charge per unit volume of any charged bulk matter is called volume charge density.$\\$Its unit is coulomb per cubic meter (C$m^{-3}$ )$\\$$ρ=\frac{q}{V} \\$

## Coulombs Law:

1. Description$\\$The force of attraction or repulsion between two point charges is directly proportional to the product of charge$\\$and inversely proportional to the square of the distance between them.$\\$■F∝$\frac{q_1.q_2}{r^2}$$\\$or,F=$\frac{q_1.q_2}{4πε_or^2} \\$Where $\frac{1}{4πε_0}=9×10^9 Nm^2 C^{-2}$ and$\\$$ε_o =8.85×10^{-12}{C^2}$ or$\\$Farad/meter is called permittivity of free space.$\\$$F_{medium} =\frac{1}{4πε}\frac{q_1.q_2}{r^2} \\$So,$ε_r=\frac{F_{air}} {F_{medium}} " where " ε_r=\frac{ε}{ε_0}$