Anna University Coimbatore 2009 B.E Electrical and Electronics Engineering Ee1302- electromagnetic theory - Question Paper

AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY

Dept. of Electrical and Electronics Engineering

EE1302- ELECTROMAGNETIC THEORY

Prepared by: R.Subramanian

QUESTION BANK

UNIT I VECTOR FUNCTIONS AND CO-ORDINATE SYSTEMS

PART A

1.      What are the sources of electro magnetic fields?

2.      Transform a vector A=ya_x-xa_y+za_z into cylindrical coordinates.

3.      How the unit vectors are defined in cylindrical co-ordinate systems?

4.      What is the physical significance of the term divergence of a vector field?

5.      Define scalar triple product and state its characteristics.

6.      Give the relation between Cartesian and cylindrical co-ordinate systems

7.      Define curl.

8.      What is unit vector? What is its function while representing a vector?

9.      Which are the differential elements in Cartesian co-ordinate system?

10.  What is the physical significance of divergence?

11.  Define Surface Integral.

12.  Sketch a differential volume element in cylindrical co-ordinates resulting from differential changes in three orthogonal co-ordinate directions.

13.  What is volume charge density?

14.  Define Line Integral.

15.  Calculate the total charge enclosed by a circle of 2m sides, centred at the origin and with the edge s parallel to the axes when the electric flux density over the cube is D=10x³/3a_x(C/m²)

16.  State stokes theorem.

17.  Give practical examples for diverging and curling fields.

18.  State Divergence theorem and mention the significance of the theorem.

19.  A vector field F = (1/ r) a_r in spherical co-ordinates. Determine F in Cartesian form at a point x =1, y =1 and z = 1.

20.  Given A= 10 a_y + 3a_z and B = 5a_x + 4a_y , find the projection of A on B

21.  Prove that curl gradΦ = 0.

22.  Verify that the vectors A = 4a_x 2a_y + 2a_z and B = -6a_x + 3a_y 3a_z are parallel to each other.

23.  What are different co-ordinate systems?

24.  The temperature in an auditorium is given by T= x² + y² z. A mosquito located at (1, 1, 2) desires to fly in such a direction that it will get warm as soon as possible. In what direction it must fly?

PART B

1. (i) Explain the electric field distribution inside and outside a conductor

(ii) Explain the principle of electrostatic shielding.

(iii) Draw the equipotent lines and E lines inside and around a metal sphere.

2. i) State and prove Divergence theorem.

ii) State and prove Stokes theorem.

3. Given A = a_x + a_y, B = a_x + 2a_z and C = 2 a_y + a_z . Find (A X B) X C and compare

it with A X (B X C). Using the above vectors, find A.B X C and compare it with

A X B.C.

4. Find the value of the constant a, b, c so that the vector E = (x + 2y + az) a_x +

(bx 3y 2) a_y + (4x + cy + 2z) a_z is irrotational.

5. Using the Divergence theory, evaluate ∫∫ E.ds = 4xz a_x y² a_y + yz a_z over the cube bounded by x = 0; x = 1; y = 0; y = 1; z = 0; z = 1.
6. Explain the spherical co-ordinate system?
7. (i) Use the cylindrical coordinate system to find the area of the curved surface of a

right circular cylinder where r = 20 m, h = 5m and 30120 .

(ii)State and explain Divergence theorem.

8. (i) Derive the stokes theorem and give any one application of the theorem in electromagnetic fields

(ii)Obtain the spherical coordinates of 10a_x at the point P (x = -3, y = 2, z = 4).

9. Find the charge in the volume

If ρ = 10 x² y z μC/m³.

10. (i) Determine the constant c such that the vector F = (x + ay)i + (y + bz)j +

(x + cz)k will be solenoidal.

(ii) Given in cylindrical co-ordinate. For the contour shown

in Fig.Q-32, verify Stokes theorm.

Fig.Q-32.

11. Verify Stokes theorem for a vector field F = ρ²cos² Φa_ρ+zsinΦa_z around the

path L defined by 0≤ ρ ≤ 3, 0≤ Φ ≤ 45^o and z = 0.

12. i) What are the major sources of Electromagnetic fields (any five)?

ii) What are the positive and negativeeffcts of EM fields on living things?

iii) What are the E and H field limits for public exposure?

iv)Give any one example to reduce the effect of EM field.

13. Verify the divergence theorem for a vector field A = xy² a_x+y³ a_y+y²z a_z and

the surface is a cuboid defined by 0<x<1, 0<y<1, 0<z<1.

14. Given that F = x² y a_x - ya_y. Find ∫ F. dl for the closed path shown in figure

and also verify Stokes theorem.

15. i) Given A = 5a_x and B = 4a_x + t a_y ; Find t such that the angle between A and

B is 45˚

ii) Using the Divergence theorem, evaluate ∫∫ A.dS = 2xy a_x + y² a_y + 4yz a_z over the

cube bounded by x = 0; x = 1; y = 0; y = 1; z = 0; z = 1.

16. i) Determine divergence and curl of the vector A = x² a_x + y² a_y + y² a_z.

ii) Determine the gradient of the scalar field at P (√2, π / 2, 5) defined in

cylindrical co-ordinate system as A= 25ρ sinφ.

17. a) Determine divergence and Curl of the following vector fields.

i) P= x²yz a_x + xz a_z. ii) Q = ρsinΦa_ρ + ρ²z a_Φ + zcosΦ a_z

iii) T = 1 / r² cosθ a_r + r sinθ cosθ a_θ+ cosθ a_Φ

b) Fnd the gradient of the following scalar fields

i) V = e^-z sin2x coshy ii) U = ρ²z cos 2Φ iii) W = 10r sin²θ cosΦ.

18. i) Show that the vector field A is conservative if A possesses one of the following

two properties. 1) The line integral of the tangential component of A along a

path extending from point P to point Q is independent of the path.2) The line

integral of the tangential component of A along a closed path s zero.

ii) If A = ρcosΦa_ρ + sinΦa_Φ , evaluate ∫ A.dl around the path shown in figure.

Confirm this using Stokes theorem.

19. i) A vector field is given by the expression F = (1/ρ ) a_ρ in cylindrical

co-ordinates and F = (1/r) a_r in spherical co-ordinates. Determine F in each case

in the Cartesian form at a point (1, 1, 1).

ii) If a scalar potential is given by the expression Φ = xyz, determine the potential

gradient and also prove that vector F = grad Φ is irrotational.

20.    i) Given two points A (2, 3,-1) and B (4, 25˚, 120˚). Find the spherical and

cylindrical co- ordinates of point A and Cartesian and cylindrical co-ordinates

of point B.

ii) Find the curl of H at P (2, Π/6, 0), where H = 2ρ cosφ a_ρ - 4ρ sinφ a_φ + 3a_z.

UNIT II ELECTRIC FIELDS

PART A

1. State coulombs law.

2. What are the different types of charges?

3. State Gauss Law.

4. Draw the equipotential lines and electric field lines for a parallel plate capacitor.

5. Define dielectric strength. What is the dielectric strength of co-axial cable?

6. Write and explain the coulombs law in vector form.

7. Define electric field intensity at a point.

8. What is the electric field around a long transmission line?

9. Sketch the electric field lines due to an isolated point charge Q.

10. A uniform line charge with P_L = 5 c/m lies along the x-axis. Find E at (3,2,1).

11. What are the various types of charge distributions, give an example of each.

12. Define Dielectric strength of a material. Mention the same for air.

13.  Write and explain the coulombs law in vector form.

14.  Using Gausss law, derive the capacitance of a coaxial cable.

15.  Write down Poissons and Laplaces equation.

16.  Calculate the total charge enclosed by a cube of 2m side, centered at the origin and with the edges parallel to the axes when the electric flux density over the cube is

D = 10x³ / 3 a_x C / m².

17. Define dielectric strength of a material and mention the same for air.

18. The electric potential near the origin of the system is V = ax² + by² + cz². find the

electric field at (1, 2, 3).

19. What are symmetrical charge distributions?

20. Define dipole moment.

21. An infinite line charge charged uniformly with a line charge density of 20 nC / m

is located along z- axis. Fine E at (6, 8, 3) m.

22. Define electric potential and potential difference.

23. Using Gausss law, derive the capacitance of the co-axial cable.

24. Derive Poissons equation.

25. Two point charges q1 and Q2 are located at (1, 2, 0) and (2, 0, 0) respectively.

Find the relation between Q1 and Q2 such that the total charge at the point

P (-1, 1, 0) will have no x- component).

26. Verify the following potential satisfy Laplaces equation V= 15 x² yz 5 y³z.

27. A spherical capacitor consists of an inner conducting sphere of radius Ri and an

outer conductor with a spherical inner wall of radius Ro. The space in between is

filled with dielectric of permittivity ε. Determine the capacitance.

28.  What is the capacitance of co-axial cable?

29.  Write the continuity equation.

30.  Why Gausss law cant be applied to determine the electric field due to finite line charge?

31.  A uniform surface charge of σ = 2 μC / m² is situated at z=2 plane. What is the value of flux density at P (1, 1, 1) m.

UNIT II

PART B

1. State and explain the experimental law of coulomb?

2. State and prove Gauss law and write about the applications of Gauss law?

3. State and explain Gausss law. Derive an expression for the potential at a point outside a

hollow sphere having a uniform charge density

4. (i) A circular disc of radius a, m is charged uniformly with a charge density of σ C/m²

Find the electric field intensity at a point h, m from the disc along its axis.

(ii) A circular disc of 10 cm radius is charged uniformly with a total charge of 10^-6c.

Find the electric intensity at a point 30 cm away from the disc along the axis.

5. A line charge of uniform density q C / m extends from the point (0, -a) to the point (0, 1)

in the x-y plane. Determine the electric field intensity E at the point (a, 0).

6. Define the electric potential, show that in an electric field, the potential difference

between two points a and b along the path, V_a V_b = -

7. What is dipole moment? Obtain expression for the potential and field due to an electric

dipole.Two point charges Q₁ = 4nC₁, Q = 2nC are kept at (2, 0, 0) and (6, 0, 0).Express

the electric field at (4, -1, 2)

8. Derive the electric field and potential distribution and the capacitance per unit

length of a coaxial cable.

9. Explain in detail the behavior of a dielectric medium in electric field.

10. i)Discuss Electric field in free space, dielectric and in conductor.

ii) Determine the electric field intensity at P ( -0.2,0,-2.3) due to a point charge of

5 nC at (0.2, 0.1, -2.5) in air.

11.(i) Derive the electrostatic boundary conditions at the interface of two deictic media.

(ii) If a conductor replaces the second dielectric, what will be the potential and electric

field inside and outside the conductor?

12. (i) Derive the expression for scalar potential due to a point charge and a ring charge.

(ii) A total charge of 100 nC is uniformly distributed around a circular ring of 1.0m

radius. Find the potential at a point on the axis 5.0 m above the plane of the ring.

Compare with the result where all charges are at the origin in the form of a point

charge.

13. (i) Derive the expression for energy density in electrostatic fields.

(ii) A capacitor consists of squared two metal plates each 100 cm side placed parallel and 2 mm apart. The space between the plates is filled with a dielectric having a relative permittivity of 3.5. A potential drop of 500 V is maintained between the plates. Calculate i) the capacitance, ii) the charge of capacitor, iii) the electric flux density, iv) the potential gradient

14. A uniformly distributed line charge, 2m long, with a total charge of 4 nC is in

alignment with z axis, the mid point of the line being 2 m above the origin. Find the

electric field E at a point along X axis 2 m away from the origin. Repeat for

concentrated charge of 4 nC on the z axis 2 m from the origin, compare the results.

15. (i) Define the potential difference and absolute potential. Give the relation between

potential and field intensity.

(ii) Two point charges of +1C each are situated at (1, 0, 0) m and (-1, 0, 0) m. At what

point along Y axis should a charge of -0.5 C be placed in order that the electric

field E = 0 at (0, 1, 0) m?

16. If V = [2 x²y + 20z 4 / (x² + y²)] volts, find E and D at P (6,-2.5, 3).

17. Derive an expression for capacitance of a spherical capacitor with conducting shells

Of radius a and b.

18. Obtain an expression for energy stored and and energy density in a capacitor.

19. Conducting spherical shells with radii a = 10 cm and b= 30 cm are maintained at

potential difference of 100 V such that V(r = b) = 0 and V(r = a) = 100 V. Determine

V and E in region between shells.

20. A total charge of 10^-8 C is distributed uniformly along a ring of radius 5m. Calculate

the potential on the axis of the ring at a point 5m from the centre of the ring.

21. Two parallel plates with uniform surface charge densities equal and opposite to each

other have an area of 2 m2 and distance of separation of 2.5 mm in free space. A

steady potential of 200 V is applied across the capacitor formed. If a dielectric of

width 1 mm and relative permittivity 2 is inserted into this arrangement what is the

new capacitance formed?

22. i) Derive Poissons and Laplaces equation and explain their significance in field

theory.

ii) Three concentrated charges of 0.25 μC are located at the vertices of an equilateral

triangle of 10 cm side. Find the magnitude and direction of the force one charge

due to the other two charges.

23. A positive charge Q is located at the centre of a spherical conducting shell of inner

radius Ri and outer radius Ro. Determine E and V as function of radial distance R.

24. i) Write a note on dielectrics.

ii) Find the electric field intensity at the point (0, 0, 5) m due to Q1 = 0.35μC at

(0, 4, 0) and q2 =-0.55 μC at (3, 0, 0) m.

25. The electric flux density is given as D= r/4 a_r nC / m2 in free space. Calaculate E

at r = 0.25 m, the total charge within the sphere of r = 0.25m and the total flux

leaving the sphere of r = 0.35m.

26. An infinitely long uniform line charge is located at y=3, z=5. If ρ_L= 30 nC/m. Find

field intensity E at: i) origin ii) P (0, 6,) and iii) Q (5, 6, 1).

UNIT III - MAGNETIC FIELDS

PART A

1. State BiotSavarts law.
2. Distinguish magnetic scalar potential and magnetic vector potential.
3. Plane y=0 carries a uniform current of 30 a_z mA/m. Calculate the manetic field intensity at (1, 10,-2) m in rectangular coordinate system.
4. Plot the variation of H inside and outside a circular conductor with uniform current density.
5. What is vector A?
6. State Amperes Law.
7. What is the relation between magnetic field density B and vector potential A?
8. State the significance of E and H. Give an example of this.
9. What is magnetic boundary condition?
10. Draw the magnetic field pattern in and around a solenoid.
11. What is H due to a long straight current carrying conductor?
12. Calculate inductance of a ring shaped coil having a mean diameter of 20 cm wound on a wooden core of 2 cm diameter. The winding is uniformly distributed and contains 200 turns.
13. A conductor located at x=0.5 m , y=0 and 0<z<2.0 m carries a current of 10 A in the a_z direction. Along the length of the conductor B=2.5 a_x T. Find the torque about the x axis.
14. What do you mean by magnetic moment?
15. Define mutual inductance.
16. Plot the variation of H inside and outside a circular conductor with uniform current density.
17. A long straight wire carries a current I = 1 A. At what distance s the magnetic field H = 1 A/m.
18. Write the expression for magnetic force when charge particle moves in a magnetic field.
19. State Amperes circuital law.
20. Write down the magnetic boundary conditions.
21. Define magnetic moment and magnetic permeability.
22. Draw the magnetic field pattern inside and outside the circular conductor with uniform current density.
23. What is the relation between magnetic flux density B and vector potential A?
24. Compare steady current and steady state current.
25. What is Lorentz law of force and writethe equation.?
26. Calculate h at (3,-6,2) due to a current element of length 2 mm located at the origin in free space that carries current 16 mA in +Y direction.
27. An infinitely long straight conductor with circular cross section of radius b carries steady current I. determine the magnetic flux density inside the conductor.
28. A small circular loop of radius 10 cm is centered at origin and placed on the Z = 0 plane. If the loop carries a current of 1 A along a_Φ. Calculate magnetic moment of the loop.
29. Define magnetic susceptibility.
30. What do you mean by magnetization?
31. State the boundary conditions of magnetic media.
32. State the modified form of expression curl H = ▼x H = J, if the contour does not enclose any current, then how is vector H expressed with scalar magnetic potential.
33. What is solenoid?
34. Classify the magnetic materials.

UNIT III

PART B

1. (i) Use Biot Savarts law to find magnetic field intensity for finite length of

conductor at a point P on Y axis.

(ii)A steady current of I flows in a conductor bent in the form of a square

loop of side a. Find the magnetic field intensity at the centre of the

current loop.

iii) Find the magnetic field intensity at the centre of a square of sides equal to 5m

and carrying 10 A current.

2. (i) when a current carrying wire is placed in an uniform magnetic field,

show that torque acting on it is T=X

(ii) A magnetic circuit comprising a toroid of 5000 turns and an area of 6cm²

and mean radius of 15 cm carries a current of 4A. Find the reluctance

and flux given μ_r = 1.

3. Calculate B due to a long solenoid and a thin toroid.

4. (i) Derive for force and torque in a magnetic field using motor as an example.

(ii) Find the torque about the y axis for the two conductors of length l, carrying

current in opposite directions, separated by a fixed distance w, in the uniform

magnetic field in x direction.

5. (i) Explain magnetization in magnetic materials and explain how the effect of

magnetization is taken into account in the calculation of B/H.

(ii) Find H in a magnetic material

1. When = 0.000018 H/m and H = 120 A/m.
2. When B = 300 T and magnetic susceptibility = 20.

6. a) Derive the magnetic force between two parallel conductors carrying equal

current in the (i) Same direction (ii) opposite direction

b) Two wires carrying currents in the same direction of 5000 A and 10000 A are

placed with their axes 5 cm apart. Calculate the force between them.

7. (i) Find the field intensity at a point due to a straight conductor carrying current I

as shown in Fig.Q-7.

Fig.Q-7

(ii) Find H at the centre of an equilateral triangular loop of side 4 m carrying

current of 5 A.

8. (i) Derive the expression for co-efficient of coupling in terms of mutual and self

inductances.

(ii) An iron ring with a cross sectional area of 3 cm² and a mean circumference of

15 cm is wound with 250 turns wire carrying a current of 0.3 A. The relative

permeability of the ring is 1500. Calculate the flux established in the ring.

If a saw cut of width 2mm is made in the above ring, find the new value of flux

in the circuit.

9. Develop an expression for magnetic field intensity inside and outside a solid

cylindrical conductor of radius a, carrying a current I with uniform density.

Sketch the variation of the field intensity.

10. Derive H due to a circular current loop and extend the same to compute H due to a

long solenoid.

11. i)State and prove Amperes circuital law.

ii) State and explain Biot- Savarts law

12. i) Obtain an expression for magnetic vector potential.

ii) Give a brief note on magnetic materials.

13. At a point P (x,y,z) the components of vector magnetic potential A are given as

A_x = (4x + 3y+2z); A_y = (5x + 6y +3z) and Az = (2x + 3y +5z). Determine B at

point P.

14. Derive the boundary conditions between two magnetic media.

15. A solenoid has an inductance of 20 mH. If the length of the solenoid is increased by

two times and the radius is decreased to half of its original value, find the new

inductance.

16. Write short notes on Magnetic vector potential, Biot- Savarts law, Lorentz law of

force and Magnetic energy density.

17. An iron ring with a cross sectional area of 8 cm² and a mean circumference of

120 cm is wound with 480 turns wire carrying a current of 2 A. The relative

permeability of the ring is 1250. Calculate the flux established in the ring.

18. A uniform cylindrical coil of 2000 turns is 60 m long and 5 cm diameter. If the coil

carries a current of 10 mA, find the magnetic flux density at the centre of the coil, on

the axis at one end of the coil and on the axis halfway between centre and one end of

the coil.

19. A circular loop located on x² + y² = 9, z=0 carries a direct current of 10 A along a_Φ.

Determine H at (0, 0, 4) and (0, 0, -4).

20. A small current loop L1 with magnetic moment 5 a_z Am² is located at the origin

while another small loop current L2 with magnetic moment 3 a_y Am2 is located at

(4, -3, 10). Determine the torque on L2.

21. i) Find the maximum torque on an 85 turns, rectangular coil with dimension

(0.2 x 0.30) m, carrying current of 5A in a field B= 6.5 T

ii) Derive an expression for magnetic vector potential.

22. i) Derive an expression for the inductance of solenoid.

ii) Derive the boundary conditions at an interface between two magnetic media.

23. Determine the force per unit length between two long parallel wires A and B

separated by 5 cm in air and carrying currents of 40 A in the same direction and inthe

opposite direction.

24. Derive the expression for curl H = J.

25. Explain the concepts of scalar and vector magnetic potential.

UNIT IV- MAXWELLS EQUATIONS

PART A

1. Write point form or differential form of Maxwells equation using faradays law.
2. Explain why X E = 0.
3. Write the Maxwells equation from faradays law both in integral and point forms.
4. Compare field theory with circuit theory.
5. What is motional emf?
6. Mention the limitation of circuit theory.
7. Write down the expression for the emf induced in the moving loop in static B field.
8. State Faradays law.
9. Distinguish between transformer EMF and motional EMF.
10. What is displacement current density?
11. Time varying field is not conservative.Prove it.
12. Write the EMF equation for moving conducting loop in a time varying field.

UNIT IV

PART B

1. (i) Summarize Maxwells equation for time varying fields in integral and

differential form.

(ii) Compare the magnitude of conduction current density and displacement

current density in a good conductor in which σ = 10⁷ S/m, Єr = 1 when

E = 1sin 120πt. Comment on the result.

2. (i) Derive Maxwells equation for E and H.

(ii) Explain (a) Motional emf. (b) Transformer emf.

3. Explain the different methods of emf induction with necessary governing

equations and with suitable examples.

4. (i) Write short notes on Faradays laws of electromagnetic induction.

(ii) What do you by displacement current? Write down the expression for the total

current density.

5. Explain the relationship between the field theory and circuit theory using a simple

RLC series circuit. Also explain the limitations of the circuit theory.

6. i) A straight conductor of length 40 cm moves perpendicularly to its axis at a velocity

of 50 m/s in a uniform magnetic field of flux density 1.2 T. Evaluate the emf

induced in the conductor if the direction of motion is

-          normal to the field

-          parallel to the field

-          at an angle 60^o to the orientation of the field.

ii) A circular cross section conductor of radius 2mm carries a current i_c = 2.5 sin

(5x 10⁸t) A.What is the amplitude of displacement current density if

σ = 35 MS/m and ε_r = 1.

7. Differentiate conduction and displacement current and derive the same .Explain the

need of displacement current in Maxwells equations.

8.i) Do the fields E = E_m sinx sint a_y and H = E_m/μ_o cos x cos t a_y , satisfy Maxwells

equations.

ii) Find the amplitude of displacement current density in the air near car antenna

where the field strength of EM signal E = 80 cos (6.277 x 10⁸ t 2.092 y ) a_z V/m.

9.From the fundamental laws , derive the Maxwells equations and the need for the

Maxwells contributions in both differential and integral form.

10.i) Discuss the relation between field theory and circuit theory. (8)

ii) In free space H = 0.2 cos (ωt βx ) a_z A/ m. Find the total power passing through

a circular disc of radius 5 cm.

11. State and explain Faradays law of electromagnetic induction. Hence derive the

expressions for statically and dynamically induced emfs.

12. A circular loop of N turns of conducting wire lies in the xy plane with its centre at

the origin of a magnetic field specified by B = Bo cos (πr / 2b ) sin ωt where b is

the radius of the loop and ω is the angular frequency. Find the mf induce din the

loop.

13. i ) derive modified form of Amperes circuital law in intehral and differential forms,

ii) Find the amplitude of displacement current density inside a capacitor where

ε_r = 600 and D = 3 x 10^-6 (sin ( 6 x 10⁶ t 0.3464x ) a_z C/m² .

14. i) A square coil loop area 0.01 m² and 50 turns is rotated about its axis at right

angles to a uniform magnetic field B = 1 T. Calculate the instantaneous value of

EMF induced in the coil when its plane is at right angles to the field, at 45 deg to

the field and in the plane of the field. Speed of rotation is 1000 rpm.

ii) A conducting cylinder of radius 5 cm, height 20 cm rotates at 600 rev / sec in a

radial field B = 0.5 T. Sliding contacts at the top and bottom are connected to

Voltmeter. Find the induced voltage.

15. What is displacement current? Show that the displacement current in the dielectric

Parallel plate capacitor is equal to the conduction current in the leads.

17.  i) The conduction current flowing through a wire with conductivity σ = 3 x 10⁷ S/m

and ε_r =1 is given by I_c = 3 sin ωt mA. If ω = 10⁸ rad / sec. Find the displacement

current.

ii) The magnetic field intensity in free space is given as H = H_o sinθ a_y A/m, where

θ = ωt = βz and β is a constant. Determine the current density vector J.

UNIT V- ELECTROMAGNETIC WAVES

PART A

1. State wave equation in phasor form.
2. Given E(z,t) = 100 sin (wt-βz)a_y(V/m) in free space, sketch E and H at t=0.
3. Define Poynting vector.
4. Find the average power loss/volume for a dielectric having, ε_r=2 and tanδ = 0.005, if E = 1.0 kV/m at 500 MHz.
5. Calculate the skin depth and wave velocity at 2 MHz in Aluminum with conductivity 40 MS/m and _r=1.
6. Given E = Emsin (wt-βz)a_y in free space, sketch E and H at t=0.
7. Derive an expression for loss tangent in an insulating material and mention the practical significance of the same.
8. A medium has constant conductivity of 0.1 mho/m, _r=1, ε_r=30. When these parameters do not change with the frequency, check whether the medium behaves like a conductor or a dielectric at 50 kHz and 10 GHz.
9. In free space E(z,t) = 100 sin (wt-βz)a_x (V/m). Find the total power passing through a square area of side 25 mm, in the z=0 plane.
10. Define skin depth.
11. Find the velocity of a plane wave in a lossless medium having =10, ε_r=20.
12. What do you mean by depth of penetration?
13. For a lossy dielectric material having _r=1, ε_r=48, σ=20 s/m. Calculate the propagation constant at a frequency of 16 GHz.
14. What is the velocity of electromagnetic wave in free space and in lossless dielectric?
15. Define a Wave.
16. What is skin effect?

UNIT V

PART B

1. (i)Discuss the parameters : , V_phase and V _group.

ii) Define Brewster angle and discuss the Brewster angle and degree of

polarization.

3.      What is Poynting vector? Explain. Derive pointing theorem.

3. (i) Explain when and how an electromagnetic wave is generated.

(ii) Derive the electromagnetic wave equations in free space and mention the types

of solutions.

4. A plane wave propagating through a medium with _r=2, ε_r=8 has

E = 0.5 sin (10⁸ t-β_z)a_z (V/m). Determine (i) β (ii) The loss tangent (iii) wave

Impedance (iv) wave velocity (v) H field

5. A plane traveling wave has a peak electric field intensity E as 6 kV/m. If the

medium is lossless with _r=1, ε_r=3, find the velocity of the EM wave , peak

POYNTING vector, impedance of the medium and the peak value of the magnetic

field H. Derive all the formulae used.

6. Determine the amplitude of the reflected ad transmitted E and H at the interface of

two media with the following properties. Medium 1: _r=1, ε_r=8.5,σ = 1.

Medium 2: free space. Assume normal incidence and the amplitude of E in the

medium 1 at the interface is 1.5 mV/m. Derive all the formulae used.

7.      (i) Derive the electromagnetic wave equation in frequency domain and the

propagation constant and intrinsic impedance.

(ii) Explain the propagation of EM waves inside the conductor.

8. Define and derive skin depth. Calculate skin depth for a medium with conductivity

100 mho/m, _r=2, ε_r=3 at 50Hz, 1MHz and 1 GHz.

9. In free space E (z,t) = 100 cos (wt-bz)a_x(V/m). Calculate H and plot E and H

waveforms at t=0.

10. Derive the transmission and reflection coefficients at the interface of two media

for normal incidence. Discuss the above for an open and a short circuited line.

11. A free space silver interface has E (incident) = 100 V/m in the free space side.

The frequency is 15 MHz and the silver constants are _r=1, ε_r=1, σ=61.7 MS/m.

Determine E (reflected), E (transmitted) at the interface.

12. Calculate intrinsic impedance η, propagation constant γ and wave velocity υ for a

conducting medium in which σ = 58 S / m, _r=1, ε_r=1 at a frequency of 100 MHz.