LEC 24 Laplace equation | HC VERMA | GDS K S

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HC VERMA

Coulomb's law and its limitation, Electrostatic charge distribution, Linear, surface, and volume charge distributions. Use of Dirac delta function to describe point charges, linear charges and surface charges, vector expressions for electric field due to different kinds of charge distributions.
Spherical and Cylindrical coordinates, line element, surface element, and volume element. Evaluation of electric field using such coordinate systems.
Gauss's law in differential form, Concept of divergence, Expressions in Cartesian, spherical and cylindrical coordinates, Evaluation of charge density from the electric field, Integral form of Gauss's law, calculation of electric field for planer, spherically and cylindrically symmetric charge distributions.
Electric potential energy and potential, Concepts of Curl and gradient, Relation between E and V, Potential due to a continuous charge distribution, Energy in an electric field, Boundary conditions on the electric field across a surface.
Multipole expansion of potential. Monopole, Electric dipole moment, Field due to a dipole, force, and torque due to E-field on a dipole, Quadrupole moment of a charge distribution.
Charge distribution on conductors, Cavities in a conductor, capacitors.
Laplace and Poisson's equations, Properties of solutions of Laplace equation, Uniqueness theorems.
Method of images, general theory, charge in front of conductors of different shapes.
Dielectrics, Polarization P in a dielectric, Bound and free charges, Relation with polarization, Electric
field due to a uniformly polarized sphere, Electrical susceptibility.
Displacement vector D, Gauss's law in terms of D, Boundary conditions on D.
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