CD Transform the vector R zaz into Cartesian coordinate system.

Determine the divergence of the vector A at the point where
A =yzax 4xyay yaz

Prove the following identity: x x x

State Coulomb's law and express it mathematically.

Define the term 'electric field intensity'. An infinitely long line charge of uniform density ALC/m is situated along z-axis. Derive the expression for the electric field intensity at a point z).

3. Derive the expression for the capacitance of a cylindrical capacitor of length formed by two coaxial cylinders of radii and by

using Gauss law.

using Laplace's equation.

State and explain Ampere's circuital law. Express it in integral form.

The inner and outer radii of a long hollow cylindrical conductor with its axis along the z-axis of cylindrical coordinates are 4·0 mm and 6.0 mm respectively. The current in the conductor is 150 A. Calculate the magnetic field intensity vector at r 3·0 mm, 5·0 mm and 7·0 mm.

Write Maxwell's equations for time varying fields in differential form. From the set obtain the integral form of the equations.

Give the physical meanings of each equation.

Derive the relationship between E and H for a uniform plane wave and show that E and H are transverse.

State Poynting theorem and express it mathematically.

7. Derive the expression for reflection coefficient and transmission coefficient for a uniform plane wave incident normally on the boundary surface between any two media characterised by intrinsic impedances Z1 and Z2. Hence obtain the relationship between reflection coefficient and standing wave ratio.

List the simplifying assumptions which are made to study wave propagation in the rectangular wave guide.

Define TEM waves and explain why TEM waves cannot exist in a single. hollow metallic conductor.

9. Make a comparison between the following:

Divergence of a vector and Curl of a vector

Displacement current and Conduction current

10. Write notes on any two of the following:

Poisson's equation

Boundary conditions for magnetic field

Propagation of plane wave in lossy dielectric