Electrostatics

Objectives

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• Historical background of electricity and magnetism • The role of electrostatic force in day – to-day life • Coulomb’s law and superposition principle • The concept of electric field • Calculation of electric field for various charge configurations • Electrostatic potential and electrostatic potential energy • Electric dipole and dipole moment • Electric field and electrostatic potential for a dipole • Electric flux • Gauss law and its various applications • Electrostatic properties of conductors and dielectrics • Polarisation • Capacitors in series and parallel combinations • Effect of a dielectric in a capacitor • Distribution of charges in conductors, corona discharge • Working of a Van de Graaff generator

Summary

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„ Like charges repel and unlike charges attract „ The total charge in the universe is conserved „ Charge is quantized. Total charge in an object q = ne where n = 0,1,2,3… and e is charge of the electron. „ Coulomb’s law in vector form: F q q r = r 1 4 1 2 2 πe  (r is unit vector along joining q1 , q2 ) „ Electrostatic force obeys the superposition principle. „ Electric field at a distance r from a point charge: E q r = r 1 4 2 πe  „ Electric field lines starts at a positive charge and end at a negative charge or at infinity „ Electric field due to electric dipole at points on the axial line : E p r tot =           1 4 2 3 πe „ Electric field due to electric dipole at points on the equatorial line: E p r tot = −           1 4 3 πe „ Torque experienced by a dipole in a uniform electric field:    τ = ×p E „ Electrostatic potential at a distance r from the point charge: V q r = 1 4πe „ Electrostatic potential due to an electric dipole: V p r r = 1 ⋅ 4 2 πe  „ The electrostatic potential is the same at all points on an equipotential surface. „ The relation between electric field and electrostatic potential:  E V x i V y j V z = − k ∂ ∂ + ∂ ∂ + ∂ ∂              „ Electrostatic potential energy for system of charges is equal to the work done to arrange the charges in the given configuration. „ Electrostatic potential energy of a dipole system in a uniform electric field: U p = − ⋅E   „ The total electric flux through a closed surface : ΦE Q = e where Q is the net charge enclosed by the surface „ Electric field due to a charged infinite wire : E r = r 1 2π λ e  „ Electric field due to a charged infinite plane : E n = σ 2e  (n is normal to the plane) „ Electric field inside a charged spherical shell is zero. For points outside: E Q r = r Electric field inside a conductor is zero. The electric field at the surface of the conductor is normal to the surface and has magnitude E = σ e . „ The surface of the conductor has the same potential, at all points on the surface. „ Conductor can be charged using the process of induction. „ A dielectric or insulator has no free electrons. When an electric field is applied, the dielectric is polarised. „ Capacitance of a conductor is given by C Q V = . „ Capacitance of a parallel plate capacitor: C A d = e „ Electrostatic energy stored in a capacitor: U C = V 1 2 2 „ The equivalent capacitance for parallel combination is equal to the sum of individual capacitance of the capacitors. „ For a series combination: The inverse of equivalent capacitance is equal to sum of inverse of individual capacitance of capacitors. „ The distribution of charges in the conductors depends on the shape of conductor. For sharper edge, the surface charge density is greater. This principle is used in the lightning arrestor „ Van de Graaff generator is used to produce large potential difference (~107V).