Electromagnetic Field Theory

Derive the equation of voltage reflection coefficient. Prove that voltage reflection coefficient is negative of current reflection coefficient.

Derive the equation of characteristics impedance, propagation constant and ABCD parameters of a long transmission line. 

What is pointing vector. Derive the equation for the average power using pointing theorem. 

What are the characteristics of a plane wave? Derive the equation for internsic impedance for partially conducting media. 

A radial field H-cos a_r A/m (where a_r is radial unit vector) exists in a free space. Find the magnetic flux crossing the surface defined by lm and 1m in cylindrical co-ordinates.

Use Biot-Savart law to find out the magnetic field density B at (0,0,2)due to a current(I) carrying loop placed at z=0 in cylindrical co-ordinates symmetrically. Use the result to find B in a solenoid.

In spherical co-ordinates, V=-25V on a conductor at r=2cm and V=150V on second conductor at r=35cm. The space between conductors is a dielectric material of relative permittivity of 3.12. Find the surface charge densities on the conductors. 

Find the Force on a point charge of 50C at (0,0,5)m due to charge of 500C that is uniformly distributed over the circular disk of radius r=5m. The disk is placed at z=0 in cylindrical co-ordinates symmetrically. 

(g) Show that displacement current density is equals to rate of change of electric flux density. 

(f) Differentiate between phase velocity and group velocity. Give their formulas.

(e) What is a distortion-less transmission line? How its characteristics impedance is calculated. 

(d) What is depth of penetration? Write its formula for a good Conductor.

(b) What is curvilinear coordinate system and how it simplifies the easier interpretation of Cartesian, cylindrical and Spherical Coordinate systems. 

Write short note on: 

(b) Open and Short Circuited Transmission Lines.

Write short note on: 

(a) Impedance Matching.

Obtain Transmission line Equations (characteristics) for

(b) Distortionless Line (R/L=G/C)

Obtain Transmission line Equations (characteristics) for

(a) Lossless Line (R=G=0)

Discuss the following case studies for E and H fields-

(b) Reflection of a plane wave at Oblique incidence.

Discuss the following case studies for E and H fields-

(a) Reflection of a plane wave at Normal incidence

(b) In a nonmagnetic medium

Find (i) The time average power carried by the wave

(ii) The total power crossing 100cm² of plane 2x+y=-5. 

(a) State and Prove Poynting Theorem.

(b) Derive the relation for Energy stored in Magnetic fields. 

(a) Deduce the relationship between Electric Field 'E' and Electric potential 'V' with the interpretation of Maxwell's Equation. 

(b) Obtain the relation for Electric Field due to Volume charge distribution. Draw a neat sketch by showing all the parameters. 

(a) Determine the self-inductance of a coaxial cable of inner radius 'a' and outer radius 'b'.

(c) Write all the Maxwell equations in integral form.

(a) Show that the dot and cross in the triple scalar product may be interchanged that is

(b) A vector field F expressed in Cartesian coordinates as?

Evaluate the surface integral of F over the surface of the box bounded by the planes x=0, x=1, y=0, y=1 , z =0, z= 1. Verify the answer using the divergence theorem and performing a volume integration.

(a) Briefly discuss and differentiate between Curl and Dot Products.

(g) Give a brief comparison between Electric and Magnetic Dipoles relations.

(f) What is displacement current, explain the significance of this term.

(e) Sate and explain Ampere's Circuital Law.

(d) Explain that "Why Smith chart is more useful tool in solving Transmission line problems?"Give the salient features of Smith Chart

(c) State and explain Maxwell's Equations for Time varying Electromagnetic Fields.

(b) Express the relations for Surface and Volume Charge distribution in spherical coordinate system. 

(a) Explain the physical interpretation of curl and how the is term is useful in electrostatic Fields.

j) What was the inconsistency in Ampere's Law?

(b) Find the volume of sphere using a differential volume element in aspherical co-ordinate system.

(a) Find the vector form force on a charge Q1 =200C due to Q2 = -300C where Q1 is at (0,1,2)m and is at(2,0,0). 

(b) There exists a boundary between two magnetic mediums at z = 0, = 4  Ho H/m in region 1, z > 0, and  -= 7  in region 2, z < 0. If the flux density in the region 1 is B₁ = 2i_x - 3 i_y - 2 i_z. Find B2 and H2 in region 2. There is no current at the boundary.

(a) Derive the boundary conditions at the interface of two magnetic mediums with no current at the boundary.

b) Explain the Method of Images in electrostatics and apply it to derive an expression for a point charge.

a) State and explain Biot and Savart's law in magneto-statics. Apply this law to find the magnetic fields due to surface current and volume current distributions.

b) Find the Laplacian of the scalar field V=pz sin Ø+z² cos²Ø+ p².

a) Transform the vector A= to Cartesian co-ordinates system.

b) Deduce the equation of Poisson and Laplace expressing there relationship of space rate of variation of potential with the distributed charge field?

a) Give a vector function A= 

ii) Determine the constant C4 if A is also solenoidal.

a) Give a vector function A= 

i) Calculate the values of C₁, C₂, C₃ if A is irrotational.

i) Write the SI units for permittivity and permeability.

h) What is the physical significance of  in E M Waves propagating in a medium?

g) A plane wave in a homogeneous medium has E-50 sin (10^tt+2z)iy V/m. What is the direction of wave propagation and of E.

f) What is the condition for the transmission line to be distortion free?

e) What are the values of the E & H components if the EM Wave is propagating along the x-axis?

d) What is the attenuation constant if the penetration depth of an EM Wave is 2mm.

c) If F-grad [(x³+y³+z³)-3xyz). Find curl F?

b) Explain the conditions when a field is solenoidal and when irrotational.

a) The concept of displacement current was introduced by whom?