Electromagnetism

Partial derivatives, Gradient of a scalar function. Line integral of a vector field, Divergence and Curl of a vector field, Physical significance of divergence & curl and their expressions in Cartesian coordinates, Gauss divergence theorem, Stokes curl theorem, Laplacian operator, Poisson’s and Laplace’s equation. 

Magnetic forces, Invariance of charge, Electric field measured in different frames of reference, Field of a point charge moving with constant velocity, Interaction between a moving charge and other moving charges.

Ampere’s law in differential form, Magnetic Vector Potential, Poisson’s equation for vector potential, magnetic  field due to a current carrying wire and deduction of  Biot-Savart’s law.

Electric current due to an orbiting electron, Bohr Magneton, Orbital gyro magnetic ratio, Electron spin and spin magnetic moment, magnetic susceptibility, magnetic field caused by magnetized matter, Magnetization current, Free current its H field. 

Moments of a charge distribution, Atomic and molecular dipoles, Atomic Polarizability, Permanent dipole moment, Dielectrics, capacitor filled with dielectric, the potential and field due to a polarized sphere, dielectric sphere in a uniform electric field, The electric field of charge in dielectric medium and Gauss law, Relation between electric susceptibility and atomic polarizability, Polarization due to changing electric field. The bound charge current.

Faraday’s laws of electromagnetic induction, its integral and differential form, Maxwell’s displacement current, Maxwell’s equations in differential and integral form. Poynting’s theorem ,Wave equation , EM waves in a non-conducting dielectric medium, Plane monochromatic waves in a non-conducting medium, Energy flux in a plane electromagnetic wave, Radiation pressure.