Electromagnetic Theory - QB

Department o f electrical and electronics engineering

QUESTION BANK

Subject: 131302- Electromagnetic Theory

UNIT –I: INTRODUCTION

Part A  

1.        State divergence theorem.

2.       State Stoke’s theorem.

3.       What is del operator? How is it used in density curl, gradient and divergence?

4.       Define vector product of two vectors.

5.       Write down expression for x, y, z in terms of spherical co-ordinates r,θ and φ.

6.       Write down the expression for differential volume element in terms of spherical co-ordinates.

7.       What is the divergence of curl of a vector?

8.       Write expression for differential length in cylindrical and spherical co-ordinates.

9.       Find the divergence of F= x y a_x+ y x a_y + z x a_z

10.    Define a vector and its value in Cartesian co-ordinate axis.

11.    Verify that the vectors A= 4 ax - 2ay + 2az and B = -6ax + 3ay - 3az are      parallel to each other.

12.  List out the sources of electromagnetic fields.

13. When a vector field is solenoidal and irrotational.?

Part B 

14. (i) State and prove Divergence theorem.

      (ii) For a vector field A, show explicitly that ∆.∆ x A=0: that is the divergence of the curl of any vector field is zero.

       15.  (i) State and prove Stroke’s theorem.

            (ii) Show that the vector

             H = (y²- z²+3yz-2x) a_x + (3xz+2xy) a_y + (3xy- 2xz+2z) a_z is both  

        irrotational and solenoidal.

16.  Using Divergence theorem, 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

17. What is the different co-ordinate systems used to represent field vectors?  Discuss about them in brief.

18. (i) Given A= 5 a_x and B= 4 a_{x +} t a_x  Find t such that the angle between A and B is 45.

     (ii) Using Divergence theorem evaluate   ∫∫ A.ds

  where A = 2xy a_{x  +}  y² a_{y +} 4yz  a_z and S is the surface of the cube bounded by x =0 , x = 1; y = 0, y = 1; and z = 0, z = 1.

19. (i) Determine the 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, л/2, 5) defined in cylindrical co-ordination system as A = 25 r sin Ф.

20. Given point P(-2,6,3) and vector A= y a_x +  (x+z) a_y .  Evaluate A and at P in the Cartesian, cylindrical and spherical systems.

 

UNIT II: ELECTROSTATICS

Part A

1.       State coulomb’s law.

2.       State Gauss’s law.

3.       Define dipole moment.[i]

4.       Define electric flux and flux density.

5.       Define electric field intensity or electric field.

6.       What is a point charge?

7.       Write the Poisson’s and Laplace equation.

8.       Define potential and potential difference.

9.       Give the relationship between potential gradient and electric field.

10.    Define current density.

11.    State point form of Ohm’s law.

12.    Define polarization.

13.    Express the value of capacitance for a coaxial cable.

14.    What is meant by displacement current?

15.    State the boundary conditions at the interface between two perfect dielectrics.

16.    Write down the expression for the capacitance between (a) two parallel plates (b) two coaxial cylinders.

17.    Calculate the capacitance of a parallel plate capacitor having an electrode area of 100 cm².  The distance between the electrodes is 3 mm and the dielectric used has a permittivity of 3.6 the applied potential is 80 V.  Also compute the charge on the plates.

18.    An infinite line charge charged uniformly with a line charge density of 20  n C/m is located along z-axis.  Find E at (6, 8, 3) m.

Part B

19. (i) Derive an expression for electric field due to an infinite long charge from its principles.

(ii)Derive the boundary conditions at the charge interfaced of two dielectric media.

          20. Find the electric field intensity due to the presence of co-axial cable   with inner conductors of ρs c/m² and outer conductor of - ρs c/m².

21. What is dipole?  Derive the expression for potential and electric field    

intensity due to a dipole.

22.  (i) Compare and explain conduction current and displacement current.

        (ii) A circular of radius ‘a’ meter is charged uniformly with a charge density ρ_s c/m².  Find the electric field at a point ‘h’ meter from the disc along its axis.

23. A circular disc of 10cm radius is charged uniformly with a total charge of 10^-6 C.  Find the electric intensity at a point 30cm away from the disc along the axis.

24. (i) Derive the expression for electric field intensity due to a circular surface charge.

 (ii) Two parallel plates with uniform surface charge intensity 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 is inserted into this arrangement what is the new capacitance if the dielectric is a perfect    non- conductor?

25. (i) State and prove Gauss’s law.

     (ii) Derive an expression for energy density in electrostatic fields.

26. (i) Derive Poisson’s and Laplace equation.

 (ii) Three concentrated charges of 0.25 μ C are located at the  vertices of an equilateral triangle of 10 cm side.  Find the magnitude and direction of the force on one charge due to other two charges.

27. (i)  Using Laplace’s equation find the potential V between two concentric circular cylinders, if the potential on the inner cylinder of radius 0.1 cm is 0Vand that on the outer cylinder of radius 1 cm is 100 V.

       (ii) A point charge of 5 n C is located at (-3, 4,0 ) while line y = 1,     z = 1 carries uniform charge 2 n C/m.  If V =0V at O (0, 0, 0) find V at           

A (5, 0, 1)

UNITIII: MAGNETOSTATICS

Part A

1.       State Ampere’s circuital law.

2.       State Biot-Savart law.

3.       State Lorenz law of force.

4.       Define magnetic scalar potential.

5.       Write down the equation for general, Integral and point form of Ampere’s law.

6.       What is field due to toroid and solenoid?

7.       Define magnetic flux density.

8.       Write down the magnetic boundary conditions.

9.       Give the force on a current element.

10.    Define magnetic moment.

11.    Give torque on a solenoid.

12.    State Gauss’s law for magnetic field.

13.    Define magnetic dipole.

14.    Define magnetization.

15.    Define magnetic susceptibility.

16.     What are the different types of magnetic materials?

17.    What is the inductance per unit length of a long solenoid of N turns and having a length L meters? Assume that its carries a current of I amps.

18.    A parallel plate capacitor with plate area of 5 cm²   plate separation of 3 mm has a voltage 50 sin 103 t applied to its plates.  Calculate the displacement current assuming ξ= 2 ξ₀

Part B

   19. (i) Derive an expression for the force between two current  carrying wires.   

         Assume that the currents are in the same direction.

                   (ii)  State and explain Biot-Savart’s law.

           20. Obtain an expression for the magnetic field around long straight wire using

                 magnetic vector potential.

           21. (i) Obtain an expression for the magnetic flux density and field

                 intensity due to finite long current carrying conductor.

                               (ii) Give a brief note on the magnetic materials.

          

22. Derive the expression for magnetic field intensity on the axis of solenoid at a) center and b) end point of the solenoid.

23. (i) State and explain Ampere’s circuital law.

             (ii) State and prove boundary condition for magnetic field.

24. Derive an expression for the inductance of solenoid and toroid.

25. Derive an expression for the inductance per meter length of two transmission lines.

26.  Obtain the expression for energy stored in magnetic field and also

       derive an expression for magnetic energy density.

27. (i) Derive and expression for self inductance of co-axial cable.of inner radius a and outer radius radius b.

                     (ii) A circular loop located on x²+y² =9, z=0 carries a direct current

                     of 10 A along a_θ.  Determine H at (0, 0, 4)  and (0,0,-4).

        28.  An air coaxial transmission line has a solid inner conductor of radius 

               ‘a’ and very thin outer conductor of inner radius ‘b’. Determine the

                inductance per unit length of the line.

UNIT IV:   ELECTRODYNAMIC FIELDS

Part A

1.        State Faraday’s law of electromagnetic induction.

2.       Define self inductance.

3.       Define mutual inductance.

4.       Define coupling coefficient.

5.       Define reluctance.

6.       Give the expression for lifting force of an electromagnet.

7.       Give the expression for inductance of a solenoid.

8.       Give the expression for inductance of a toroid.

9.       What is energy density in the magnetic field?

10.    Define permeance.

11.    Distinguish between solenoid and toroid.

12.    Write down the general, integral and point form of Faraday’s law.

13.    Distinguish between transformer emf and motional emf.

14.    Compare the energy stored in inductor and capacitor.

15.    State Lenz’s law.

16.    Define magnetic flux.

17.    Write the Maxwell’s equations from Ampere’s law both in integral and point forms.

18.    Write the Maxwell’s equations from Faraday’s law both in integral and point forms.

19.    Write the Maxwell’s equations for free space in point form.

20.    Write the Maxwell’s equations for free space in integral form.

21.     Determine the force per unit length between two long  parallel wires separated by 5 cm in air and carrying currents of 40 A in the same direction.

Part B

22.                (i) State and explain Faraday’s law.

(ii)Compare the field theory and circuit theory.

        23. Develop an expression for induced emf of Faraday’s disc   

        generator.

24.    Derive the Maxwell’s equation for free space in integral and point forms explain.

25.    Derive Maxwell’s equation from Faraday’s law and Gauss’s law and explain them.

26.    Derive the Maxwell’s equation in phasor differential form.

27.    Derive the Maxwell’s equation in phasor integral form.

28.    Derive and explain the Maxwell’s equations in point form and integral form using Ampere’s circuital law and Faraday’s law.

UNIT V: ELECTROMAGNETIC WAVES

1.        Define a wave.

2.       Mention the properties of uniform plane wave.

3.       Define intrinsic impedance or characteristic impedance.

4.       Calculate the characteristics impedance of free space.

5.       Define propagation constant.

6.       Define skin depth.

7.       Define polarization.

8.       Define linear polarization.

9.       Define Elliptical polarization.

10.    Define pointing vector.

11.    What is complex pointing vector?

12.    State Slepian vector.

13.    State pointing theorem.

14.    State Snell’s law.

15.    What is Brewster angle?

16.    Define surface impedance.

17.    Write the wave equation in a conducting medium. 

18.    Compute the reflection and transmission coefficients of an electric field wave travelling in air and incident normally on a boundary between air and a dielectric having permittivity of 4.

19.    Calculate the depth of penetration in copper at 10 MHZ given the conductivity of copper is 5.8 x 10 ⁷ S/m and its permeability = 1.3=26 mH/m.

Part B

1.        (i) Obtain the electromagnetic wave equation for free space in terms of electric field.

(ii)Derive an expression for pointing vector.

2.       (i) Obtain the electromagnetic wave equation for free space in terms of magnetic field.

(ii) Calculate the intrinsic impedance, the propagation constant and wave velocity for a conducting medium in which σ = 58 ms/m, μ _r = 1 at a frequency of f = 100 M Hz.

3.        (i) Derive the expression for characteristic impedance from first principle.

(ii)Show that the intrinsic impedance for free space is 120π.  Derive the necessary equation.

4.       (i) Explain the wave propagation in good dielectric with necessary equation.

(ii)Define depth of penetration.  Derive its expression.

5.       (i) Derive the expressions for input impedance and standing wave ratio of transmission line.

(ii) Find the skin depth at a frequency of 1.6 MHz in aluminium 

 σ= 38.2 ms/m and μ_r = 1.

6.       (i) State and prove pointing theorem.

(ii) Define surface impedance and derive its expression.

7.       Define Brewster angle and derive its expression.  Also define loss tangent of a medium.

8.       Determine the reflection coefficient of oblique incidence in perfect dielectric for parallel polarization.

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[i]

Sri Krishna Engineering College

Panapakkam,Chennai-601 301.

Department o f electrical and electronics engineering

Classs test –I

Part A

1.       Write down expression for x,y,z in terms of spherical co-ordinates r,θ and φ.

2.       Write down the expression for differential volume element in terms of spherical co-ordinates.

3.       Verify that the vectors A= 4 ax - 2ay + 2az and B = -6ax + 3ay - 3az are      parallel to each other.

4.    List out the sources of electromagnetic fields.

5. When a vector field is solenoidal and irrotational.?

Part B

6.  (i) State and prove Stroke’s theorem.                                              [8]

     (ii) State and prove Divergence theorem. .                                      [8]

 Sri Krishna Engineering College

Panapakkam, Chennai – 601 301.

Department of Electrical and Electronics Engineering

Class Test-I

Subject:  EE 2202 Electromagnetic Theory

       Class: 2 EEE                                                                             Date: 22.7.10

       Duration: 45 min                                                                       Max Marks:25

Part A

1. Write down the expression for differential volume element in terms of spherical co-ordinates.

2. Verify that the vectors A= 4 ax - 2ay + 2az and B = -6ax + 3ay - 3az are      parallel to each other.

3.  List out the sources of electromagnetic fields.

4.  When a vector field is solenoidal and irrotational?

5.  Write down expression for x,y,z in terms of spherical co-ordinates r, θ and φ.

Part B

       6.   (i) State and prove Stroke’s theorem.                                              [8]

            (ii) State and prove Divergence theorem. .                                      [8]

Sri Krishna Engineering College

Panapakkam, Chennai – 601 301.

Department of Electrical and Electronics Engineering

Class Test-I

                               Subject: EE 2301 Power Electronics

       Class: 3 EEE                                                                      Date: : 22.7.10

       Duration: 45 min                                                                 Max Marks:25

Part A

1. What is the function of snubber circuit?
2. What is the latching current of SCR?
3.  Compare power MOSFETs with BJTs.
4. In Traics, which of the modes the sensitivity of gate is high.
5. What is meant by syncrhonisation?

                                        Part B

6. (i) Describe the different modes of operation of a thyristor with the help of its static V-I characteristics.                                   [7]

                (ii)Describe the switching characteristics of power                      MOSFETs.                                                                               [8 ]