Electromagnetic Theory (EX-504 (B)) - Important Questions

State and prove the Divergence theorem.

Explain the Cartesian and cylindrical coordinate systems with examples.

Derive the expression for electric field intensity due to an infinite line charge

Define divergence and curl of a vector field and determine divergence and curl of following vectors.

State Gauss's law and determine the total enclosed charge in a cylindrical volume for a given electric flux density $\vec{D}$.

Derive the expressions for electric potential and electric field intensity due to an electric dipole, including Laplace's and Poisson's equations.

Write and explain the equation of continuity.

Derive the equation of continuity and calculate the energy of a system of three point charges.

Write boundary value conditions for electric field and discuss capacitances for various types of capacitors.

State Biot-Savart's law and derive the expression for magnetic field intensity due to a straight current-carrying conductor/filament.

Explain Ampere's circuital law, including its point form and applications.

Define magnetic flux, magnetic flux density and magnetic field intensity and explain/derive the relation between them.

State and explain Biot-Savart's law for the magnetic field due to a current element.

Derive magnetic boundary conditions and calculate total magnetic flux crossing the surface $$\phi = \frac{\pi}{2},\ 1 \le \rho \le 2m \le o \le z \le 5m$$ if magnetic flux density $\vec{B} = \frac{\rho}{2}\hat{a}_{\phi}$.

Explain Maxwell's equations for time-varying fields in differential and integral form.

Define displacement current and state its applications.

Describe Faraday's law with a suitable diagram.

Explain vector magnetic potential and its properties.

State Faraday's law and explain transformer emf and motional emf in detail.

Discuss following in brief:

Describe the properties of electro-magnetic waves.

Explain the behavior of uniform plane waves in dielectrics versus in conductors.

For a uniform plane wave propagating in a lossy medium/dielectric, calculate propagation parameters $\alpha, \beta$, skin depth, intrinsic impedance and the associated $\vec{E}$ / $\vec{H}$ fields.

State Poynting vector theorem and discuss reflection of plane wave for normal and oblique incidence.

Derive wave equation in dielectrics and discuss polarization of waves.

Write short note :

Write technical short notes on any three of the following: