## Electrostatics

## Properties of charges:

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.$\\$

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:

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.$\\$

Induction$\\$

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.$\\$

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.$\\$

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:

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,$ε_r=\frac{F_{air}} {F_{medium}} " where " ε_r=\frac{ε}{ε_0}$