SIDDHARTH INSTITUTE OF ENGINEERING &TECHNOLOGY:: PUTTUR

ELECTRONICS & COMMUNICATON ENGINEERING

ELECTROMAGNETIC THEORY AND TRANSMISSION LINES

QUESTION BANK

UNIT I

ELECTROSTATICS

1. a) State the Coulomb’s law in SI units and indicate the parameters used in the equations with the aid

of a diagram. [L1][CO.1][6M]

b) Point charges 1 mC and - 2 mC are located at (3, 2, -1) and (—1, —1,4), respectively. Calculate

the electric force on a 10-nC charge located at (0, 3, 1) and the electric field intensity at that point.

[L1][CO.1][6M] 2. a). State and explain Gauss’s law. Apply the Gauss’s law to find the electric field intensity at any of

interest due to uniformly charged sphere of radius ‘a’ and with uniform charge distribution𝜌 𝐶/ .

[L1][CO.1][7M] b) Determine D at (4, 0, 3) if there is a point charge —5π mC at (4, 0, 0) and a line charge 3π mC/m along the y-axis. [L1][CO.1][5M]

3. a). A circular disk of radius ‘a’ is uniformly charged with 𝜌 𝐶/ . The disk lies on z=0 with it axis

along the z-axis. Derive the expression for the electric field intensity at the point (0, 0, h).

[L1][CO.1][7M]

b). An electric dipole of 100 𝑎 pC-m.is located at the origin. Find electric potential and electric field

at a point (1,𝜋 , 𝜋). [L1][CO.1][5M]

4. a). Derive the expression for Electric field intensity (�⃗� ) at any point due to finite length charge with

suitable sketches. [L4][CO.2][6M]

b). Planes x = 2 and y = -3 respectively, carry charges 10 nC/ and 15 nC/ . If the line x = 0, z =

2 carries charge 10π nC/m, calculate E at (1, 1, -1) due to the three charge distributions.

[L1][CO.1][6M] 5. a).Determine the electric field intensity due to the infinite line charge lying along z-axis with uniform

charge 𝜌𝐿 𝑐/ . [L4][CO.2][5M]

b). Given the potential V = 𝑠𝑖 𝜃𝑐 𝑠∅, [L1][CO.1][7M]

(1) Find the electric flux density D at (2, π/2, 0). (2) Calculate the work done in moving a 10µc charge from point A(l, 30°, 120°) to B(4, 90°, 60°).

6. a) Derive the Maxwell equations for electrostatic fields. [L3][CO.3][7M]

b)Apply the Gauss’s law to find the electric field intensity due to a point charge Q located at origin.

[L3][CO.3][5M]

7. Derive expressions for continuity equation and relaxation time. [L3][CO.3][12M]

8. (a) Derive an expression for energy stored in electrostatic fields. [L3][CO.3][6M]

(b) Find the capacitance of a spherical capacitor with inner conductor of radius a= 2cm,

outer conductor of radius b=8 cm with a dielectric constant 1.5. [L2] [CO.2] [6M]

9. a) Write a Laplacian equation on Cartesian, cylindrical and spherical Coordinates?

[L4][CO.2][6M]

b) Explain conduction current and derive the expression for conduction current density?

[L4][CO.2][6M]

10. derive the expressions for the following capacitors

a) parallel plate b) coaxial c) spherical [L3][CO.3][12M]

SIDDHARTH INSTITUTE OF ENGINEERING &TECHNOLOGY:: PUTTUR

ELECTRONICS & COMMUNICATON ENGINEERING

ELECTROMAGNETIC THEORY AND TRANSMISSION LINES

UNIT II

MAGNETOSTATICS

1. State Ampere’s circuital law. Apply this law to determine magnetic field intensity �⃗⃗� at any point in

free space due to (i). An infinite line current. (ii). An infinite current sheet.[L1][CO.1][12M]

2. a) State and explain the Biot-Savart’s Law. [L1][CO.1][6M]

b) A circular loop located on + = 9, z = 0 carries a direct current of 10 A along 𝑎∅. Determine

H at (0, 0, 4) and (0, 0, -4). [L1][CO.1][6M]

3. State Biot-Savart’s law. Obtain the expression for magnetic field intensity at any point in free space

due to a long current carrying conductor using Biot-Savart’s law. [L4][CO.2][12M]

4. State Ampere’s circuital law. Apply this law to determine magnetic field intensity �⃗⃗� for infinitely

long coaxial transmission line. [L1][CO.1][12M]

5. a) Explain the force due to magnetic fields. [L3][CO.3][6M]

b) Derive the expression for energy stored in magneto-static field. [L4][CO.2][6M]

6. Derive and Explain about Magnetic Scalar and Vector Potentials. [L3][CO.3][12M]

7. Explain mutual inductance. Find the self-inductance of a coaxial cable of length d with radius of a, b

for inner conductor and out conductor respectively. [L4][CO.2][12M]

8. a) Define magnetic field intensity and magnetic flux density. [L4][CO.2][6M]

b) Given the magnetic vector potential A = - /4 az Wb/m, calculate the total magnetic flux crossing

the surface ϕ = π/2, 1 ≤ p ≤2 m , 0 ≤z ≤ 5 [L1][CO.1][6M]

9. a) Define the Newton’s second law of force. How it relates to electric field intensity? Write the

relevant expressions. [L1][CO.1][6M]

b) Distinguish Electrostatics with Magneto statics. [L1][CO.1][6M]

10. a)planes z=0 and z=4 carry current K=-10axA/m and K=10axA/m, respectively. Determine H at

i) (1,1,1) ii) (0,-3,10) [L1][CO.1][6M]

b)The charged particle mass 2kg, charge 3C stars at a point(1,-2,0) with a velocity 4ax +3az m/s in an

electric field 12ax+10 ay V/m. at t=1s ,Determine [L3][CO.3][6M]

(i)Acceleration of the charged particle (ii) Its velocity

(iii)Kinetic energy (iv) Its position

SIDDHARTH INSTITUTE OF ENGINEERING &TECHNOLOGY:: PUTTUR

ELECTRONICS & COMMUNICATON ENGINEERING

ELECTROMAGNETIC THEORY AND TRANSMISSION LINES

UNIT III

MAXWELL’S EQUATIONS (FOR TIME VARYING FIELDS)

1) a) Explain Faraday’s law in detail [L1][CO.1][6M]

b) Derive the expression of Maxwell’s first equation for time varying fields using Faraday’s

law. [L3][CO.3][6M]

2. a) Why the ampere’s circuit law is not applicable for time varying fields and how can overcome

this situation using displacement current? [L3][CO.3][6M]

b) What are the conditions of tangential and normal components at boundary surface?

[L1][CO.1][6M] 3) a) What is motional emf? How can you explain motional emf with mathematical equations?

[L4][CO.2][6M]

b) A parallel-plate capacitor with plate area of 5cm2

and plate separations of 3mm has a voltage

50sin103t V applied to its plates. Calculate displacement current assuming =20

[L4][CO.1][6M]

4) a) Tabulate Maxwell’s equations in both point form and integral form. [L1][CO.2][6M]

b) Derive the boundary conditions for Dielectric-Dielectric boundary. [L1][CO.1][6M]

5) With neat diagrams explain the boundary conditions for [L1][CO.1][12M]

a) Dielectric-Conductor b) coductor-Free space

6) A conducting bar can slide freely over two conducting rails as shown in Figure, Calculate the

induced voltage in the bar [L1][CO.1][10M]

a) If the bar is stationed at y = 8 cm and B = 4 cos 106t az mWb/m

2

b) If the bar slides at a velocity u = 20 ay m/s and B = 4az mWb/m2

c) If the bar slides at a velocity u = 20ay m/s and B = 4 cos (106t- y) az mWb/m

2

7. (a) What is transformer emf? How can you explain transformer emf with mathematical equations?

[L4][CO.2][8M]

(b) Region y<0 consists perfect conductor while region y>0 is a dielectric medium (εr=2)

has shown in figure.if there is a surface charge of 2nc/m2 on the conductor. Determine E and D at

(a) A(3,-2,2) (b) B(-4,1,5) [L1][CO.1][4M]

Conductor Dielectric(εr=2)

.A

.B

8) a) The magnetic circuit of Figure has a uniform cross section of 10-3

m2. If the circuit is energized

by a current i1(t) = 3 sin 100t A in the coil of N1 = 200 turns, find the emf induced in the coil of

N2 = 100 turns. Assume that µ=500µ0 [L1][CO.1][6M]

b) Write the word statements for Maxwell’s equations [L1][CO.1][6M]

9) In a medium characterized by σ= 0, µ= µ0, =20, and E=20sin(108t-z)ay V/m, calculate and H.

[L3][CO.4][12M]

10) a) Derive the expression for displacement current density [L1][CO.1][6M]

b) In free space E= 20 cos(t-50x)𝑎 V/m. Calculate [L3][CO.4][6M]

a) 𝐽 𝑑

b) H

c)

SIDDHARTH INSTITUTE OF ENGINEERING &TECHNOLOGY:: PUTTUR

ELECTRONICS & COMMUNICATON ENGINEERING

ELECTROMAGNETIC THEORY AND TRANSMISSION LINES

UNIT IV

EM WAVE CHARACTERISTICS

1) a) Explain Different Medium Characteristics in detail. [L3][CO.4][6M]

b) Derive the Wave Equations for Perfect Dielectric Medium. [L3][CO.4][6M]

2) A uniform plane wave propagating in medium has E=2e-α

sin (108t-βz)ay V/m if the medium is

Characterized by εr=1, μr=20, and σ =3 S/m. Determine α,β, and H. 3) a) Derive the Wave Equations for a conducting medium in both Electric and Magnetic Fields.

[L4][CO.2][6M] b)A plane wave propagating through a medium with εr=8, μr=2,has E=0.5e

-z/3 sin (10

8t-βz)ax V/m.

Determine .

(a) β, (b) wave velocity (c)Intrinsic impedance [L1][CO.1][6M]

4) a) What is Uniform Plane Wave Propagation? Explain in detail. [L1][CO.1][6M]

b) Derive the solutions of the Uniform Plane Wave equation. [L3][CO.4][6M]

5) a) Prove that Characteristic impedance for Lossy Dielectric or Conducting Medium

ƞ=E/H= (jwµ/(σ+jw)) [L1][CO.1][6M]

b) Explain in detail about Complex Permittivity and Loss Tangent. [L1][CO.1][6M]

6) a) Derive the Expression for α and for a Conducting medium. [L1][CO.1][6M]

b) Explain the Concept of Reflection and Refraction of uniform Plane Waves. [L1][CO.1][6M]

7) Find the reflection coefficient and transmission coefficient for a Perfect Dielectric Medium with

Normal Incidence. [L1][CO.1][6M]

8) a) What is Brewster angle? Prove That ӨB=tan-1(2/1). [L3][CO.4][6M]

b) Explain about Surface Impedance in detail. [L1][CO.1][6M]

9) a) State and Prove the Pointing Theorem. [L3][CO.4][6M]

b) A lossy Dielectric has an intrinsic impedance of 200300 at a particular radian frequency .

If, at the frequency, the plane wave propagating through the dielectric has the magnetic field

component H= 10 e-αx

cos (t-0.5x) ay A/m find E and α.

10) What is characteristic impedance? Obtain the relation between characteristic impedance and the

propagation constant? [L1][CO.1][6M]

SIDDHARTH INSTITUTE OF ENGINEERING &TECHNOLOGY:: PUTTUR

ELECTRONICS & COMMUNICATON ENGINEERING

ELECTROMAGNETIC THEORY AND TRANSMISSION LINES

UNIT – V

TRANSMISSION LINES

1) With neat Diagram Explain the transmission line Equation. [L1][CO.5][12M]

2) Explain the Following in Detail [L1][CO51][12M]

a) Characteristic Impedance (Z0)

b) Lossless Line

c) Distortion less Line

3) Derive the Expression For [L1][CO.4][12M]

a) Input Impedance b) Standing Wave Ratio.

4) A certain transmission line 2 m long operating at =106 rad/s has α=8 dB/m, = 1 rad/m, and

Z0=60+j40 if the line is connected to source of 1000 V, Zg=40, and terminated by a load of

20+j50 determine [L1][CO.1][12M]

a) The input impedance

b) The sending-end Current

c) The current at the middle of the line.

5) a) Explain the construction of Smith Chart [L1][CO.5][6M]

b) Write the applications of Smith Chart. [L1][CO.1][6M]

6) A lossless Transmission line with Z0= 50 is 30m long and operates at 2MHz. The line is

terminated with a load ZL=60+j40 , if u=0.6c, where c is Speed of light in a Vacuum, on the

line, find the following using Smith Chart [L1][CO.5][12M]

a) The Reflection Coefficient

b) The standing wave ratio S

c) The input impedance

7) A load of 100+j150 is connected to a 75 lossless line. Find the following Using Smith chart.

a) The Reflection Coefficient [L3][CO.1][12M]

b) The standing wave ratio S

c) The Load Admittance YL

8) List out and Explain the Applications of Transmission lines in detail. [L1][CO.5][12M]

9) a) A distortion less line has Z0=60, α= 20 mNp/m, u=0.6c, where c is Speed of light in a Vacuum. Find R,L,G,C and 𝛌 at 100 MHz. [L3][CO.4][6M]

b) An air Line has a Characteristic impedance of 70 and a phase constant of 3 rad/m at

100MHz. Calculate the inductance per meter and the Capacitance per meter of the line

[L1][CO.1][6M] 10) (a) Derive the expression for characteristic impedance of a transmission line. L1][CO.4][6M]

(b) A telephone line has the following parameters: R =40 Ω/m, G = 100 mS/m, L = 0.2 µH/m, C = 0.5 nF/m. If the line is operated at 10 MHz, calculate the characteristic impedance

and velocity of the signal.

[L2][CO.5][6M]