EMTL 4 Units Important Questions

Question bank of EMTL R-13

Sreyas Institute of Engineering & TechnologyNagole ,Hyderabad-500068

Department of Electronics & Communication EngineeringIMPORTANT QUESTION BANK

Sub : Electromagnetic Theory & Transmission Lines (A40411)Faculty : Mr. P.S.S.Pavan Ganesh,M.Tech, MIETE,MISTE

AY : 2014-15 Year :IIRegulation : R-13 Sem :II

UNIT 1: ElectrostaticsPart A:Essay Questions1. Determine the Electric Field ‘E’ due to

i. Point charge Q ii. Line charge ρl iii. Surface charge ρs iv. volume charge ρv at a point distance `r' from the source.(Using coulomb’s law & Gauss’s Law)

2. (a) Define Electric field, Electric Flux density and Electric Potential from charges and explain. (b) Explain about equipotential surfaces.

3. (a) State and explain Gauss's law and prove that ∇•D = ρv. (b) Define Electric field Intensity and potential V due to point charge and line charges & explain.

4. What is an electric Dipole? Evaluate the electric field intensity due to an electric Dipole?

PSSPGanesh ECE Department, SRYS, Nagole

Question bank of EMTL R-135. (a)State and explain Coulomb's law of force and Electric field intensity due to point charge. (b) Derive the expression for the energy stored in an electrostatic field.

6. Derive the relation between E & V.

7. (a) Define the Poisson’s and Laplace's equations. (b) Obtain expression for the capacitance of

i. a parallel plate capacitor ii. a coaxial capacitor. iii. Spherical capacitor

8. (a) What is an isotropic and homogeneous medium? (b) What is a lossy and lossless medium? (c) Explain the term Conduction Current Density.

9. (a) Explain the equation of continuity of current (or) and conservation of charge. (b) Define Relaxation time and its use in EM fields in conductors.

10. Evaluate the Coulomb's force, Electric field intensity and potential due to a line charge ‘ρl’ and surface charge ‘ρs’ .



Part B: Model Problems

* A volume charge density inside a hollow sphere is ρ = 10e-20r C/m3. Find the total charge enclosed with in the sphere also find the electric flux density on the surface of the sphere.

* Find the E field intensity on the axis of a circular ring carrying a charge density ρl C/m.

* The electric flux density is given by . Find the charge enclosed with in the region 1 < r < 2; 0 < θ < Π/2 rad.

* A point charge -4 nC is situated at the origin and another point charge 6 nC is situated at (3, 2, 1). Find E and V at (1, 1, 1).

* Given Flux Density , find the total charge with in the region 1<r<2m, 1<θ<2 rad,1<φ<2rad.

* A cube of 2cm . side is centered at the origin, with its sides parallel to the axes, and contains field of 3x2 ax V/m. Find the total charge contained in the cube, and the flux coming out of one face of the cube.

* Find the potential and sketch its variation with radial distance, for a spherical shell of radius a= 3cm, having a surface density of ρs C/m2.

* Evaluate Relaxation time in Silicon with σ= 1; εr = 9.



*Let J= 400Sinθ/(r2 +4) ar A/m2. Find the total current flowing through that portion of spherical surface r= 0.8

bounded by .01π<θ<0.3 π, 0<φ<2 π.

* A conductivity cylinder with a radius of 1cm and at a potential of 20V is parallel to a conducting plane which is at zero potential. The plane is 5 cm distant from the cylinder axis. If the conductors are embedded in a perfect dielectric for which εr = 4.5, find the capacitance per unit length between cylinder and plane.

*Calculate the relaxation time for Brass material having conductivity of 1.1X107 mhos/m at 10 MHz.

* Find the capacitance of a 50cm long coaxial cable , having conductors of 4cm and 2 cm diameters, separated by a medium of relative permittivity 2.56. Also find the stored energy and field at radius of 1.5 cm in the dielectric when 10V is applied.

Part C: Short Answer Questions

1. Describe what are the sources of electric field and magnetic fields?

2. What is a point charge?

3. State coulomb’s law.

4. Define electric field intensity or electric field.

5. Give the relation between electric field intensity and electric flux density.



6. Define electric flux and flux density.

7. State Gauss law for electric fields

8. Name few applications of Gauss law in electrostatics

9. Explain Principle of superposition.

10. Write Maxwell’s equations in point and integral form for electrostatics.

11. Define potential and potential difference.

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

13. Define current density.

14. State point form of Ohm’s law.

15. Explain the Equation of Continuity.



16. Define dielectric strength.

17. What is relaxation time? Write its equation.

18. Define polarization.

19. Define dipole moment.

20. Write the Poisson’s and Laplace equations.

21. What is a capacitor?

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

23. Write down the expression for capacitance between two parallel plates.

24. Write the expression of electric field intensity for an infinite line charge.

25. Write the expression of electric field intensity for an infinite surface charge.



UNIT 2: Magneto statics & Time varying FieldsPart A:Essay Questions1. (a) Show that the magnetic field due to straight current carrying conductor of finite length AB is given by

2. (a) State and explain Maxwell's equations obtained from Faraday's and Ampere's laws and their Magnetic field concepts & relationship. (b) State and prove Ampere's circuital law.

3. Prove that the magnetomotive force around a closed path is equal to the current enclosing the path.

4. (a) State and explain Biot-Savart's Law. (b) Derive the expression for the Magnetic field Intensity along the axis of a Circular current carrying loop, located in Z = 0 plane.



5. (a) Define Ampere's force law and elaborate the analogies between `Electric' &`Magnetic' fields in a medium. (b) Show that ∇×H = J using Ampere's work law.

6. (a) Explain the force experienced by an electron charge `Q' in magnetic field `B'. (b) The equation F = Q(E + u x B) is known as Lorentz force equation. Explain its significance.

7. Deduce Biot-Savart Law consideringi. Surface Currentii. Volume Current

8. State and explain Boundary conditions for electric field at a boundary surface between a conductor and dielectric boundary.

9. (a)State and explain boundary conditions between two dielectric media.(b)What is inconsistency of Ampere’s law and how to overcome it?

10.Write Maxwells equations for Time Varying fields in integral and differential form. Discuss the difference between static fields and Time Varying fields.

11. (a) Define Maxwell's equation in point form (Differential) and Integral form for time varying fields. (b) Explain the concept of displacement current and its special applications.



Part B: Model Problems

* Find the vector magnetic field intensity at P(1,2,3) in Cartesian coordinates caused by a current filament carrying a current of 10Amp along Z-axis, if the filament extends from

* The plane Y = 2 carries current density K = 30az Amp/mt. Find the Magnetic field intensity at A(0,0,1) and B(1,3,2).

* A charged particle of mass 2 Kg and a charge 3c starts at a point (1, -2, 0) with a velocity 4ax+3az in an Electric field 12ax+10az. At time t=1sec; find

i. the acceleration of the particleii. its velocity

* A current element (ax+2ay-az)mA, located at P(-1, 2,-2) produces a Magnetic field “dH" at Q(2,2,2). Find a unit vector in the direction of “dH”, at the point Q.

* A surface current Density K = 20ax Amp/mt flows in Y = 1 plane. Find the Magnetic field intensity at (-1,3,2).



* A current filament on the z- axis carries a current of 7mA in the az direction and current sheets of 0.5 az A/m and -0.2 az are located at ρ =1 cm and ρ =0.5 cm respectively. Calculate H at ρ =0.5 cm and 1.5 cm

* A parallel plate capacitor with plate area of 5.0 cm2 and plate separation of 3.0mm has a voltage 50Sin103t V applied to its plate. Calculate the displacement current assuming ε = 2ε0.

* A circular loop conductor having radius of 0.2mt.is placed in XY plane. The loop consists of a resistance of 10 ohms. If the Magnetic field is B = Sin104t Tesla, find the current flowing in the loop.

* Given the conduction current density in Silicon as Jc = 1 mA, evaluate the displacement current density in Silicon at 1 MHz. (use σSi = 102 mhos/m; εr (Si) = 9)

* If the Magnetic flux density is B = Cos(104t).Sin(0.1x).az milli Tesla, find the magnetic flux passing through the surface Z = 0, 0 < x < 10mt., 0 < y < 3 mt. at t = 2 Microsec.

*If H= 10 Cos(108t-z)ay mA/m, Find the corresponding electric field in air, and displacement current density.

* Copper wire carries a conduction current of 1.0 Amp at 60 Hz. Determine the displacement current in the wire? Assume “εcu = ε0”; µcu = µ0; σ = 5.8 X 107mhos/m.



Part C: Short Answer Questions

1. State Biot –savarts law.

2. State Ampere circuital law

3. Write the relation between magnetic flux density and field intensity

4. Write the relation between relative permeability and susceptibility

5. Define magnetic flux density

6. Write down the magnetic boundary conditions.

7. Give the force on a current element.



8. State Gauss law for magnetic field.

9. Define magnetic dipole.

10. Define magnetization.

11. List the types of magnetic materials

12. State Faraday’s law of induction .

13. State lenz’s law

14. Give the equation of transformer emf

15. What is motional emf ?



16. What is the emf produced by moving loop in time varying field?

17. What is time harmonic field ?

18. Distinguish between Field theory and Circuit theory

19. Write Maxwell’s equation in point and integral form for good conductors.

20. What Is significance of displacement current density?



UNIT 4 &5: Transmission Lines-I &IIPart A:Essay Questions1. (a) In a transmission line, name the types of distortions that occur and explain. (b) To avoid distortion, what is the condition for a “Distortionless line” and derive an expression for the same in terms of line parameters.

2. (a) Explain the constructional features of “Smith's” chart and its importance. b)Explain how to find length and location of double stubs in transmission line matching.

3. (a) Compare the impedance matching techniques such asi. λ/4 ii. Single Stub iii. Double Stub on transmission lines.

(b) Find the value of `l1', the position of a stub and `l2' the length of the stub for matching the antenna to the line. Use Smith chart.

4. (a) Derive the expressions for the voltage and current along a Transmission line from the source end. (b) Define “Reflection Coefficient” and “Standing wave Ratio” on transmission lines. Explain their importance in Measurements.

5. (a) Explain the properties of different length's of lossless lines such as λ/8, λ/4 and λ/2. b) Explain different types of loading for transmission lines.



6. (a) Obtain an expression for the input impedance of a line of length ‘l’ terminated by a load `ZL' with a characteristic impedance Z0 and propagation constant γ.. (b) Assuming the line to be loss less line, get the Zin expression after assuming γ=jβ only.

7. (a) Using transmission lines how to obtain various impedances. Explain. (b) What is the input impedance of a short circuited loss less line whose lengths are

i. λ/8ii.λ/4iii. 3λ/8

8. (a) What is a quarter wave transformer and how is it used for matching? Explain. (b) Explain the method of measuring an unknown load impedance ZL using a slotted transmission line and VSWR with the help of Smith's chart.

9. (a) What are Primary and Secondary Parameters of a Transmission line? (b) Obtain an expression for the propagation constant of a line at ω in terms of line parameters.

10. (a) Evaluate the equivalent lumped element parameters of a lossless short circuited line of different lengths such as l = λ/8 ; l = λ/4 ; l = 5 λ/16 ; l = 3 λ/8 and l = λ /2 . b) Establish the relations for Zsc and Zoc of rf lines and sketch their variation with βl.



11. (a) Show that a loss less quarter wave length line behaves as impedance inverter and a half-wavelength line behaves as 1:1 transformer (b) Show that a lossless transmission line of different lengths can be made to behave as

i. inductance `L'ii. capacitance `C'

iii. series impedance(figure 1) and

iv. shunt impedance resonant circuits(figure 2) (either shorted or open).

12. (a) Write the basic transmission equations in terms of R,L,C,G and V & I and explain. (b) Obtain the wave equation from the basic equation and solve the same for propagation constant and characteristic impedance of the transmission line at a frequency `W' in terms of R,L,C,G.

13. Draw the equivalent circuit of lossy and lossless transmission lines, and account for the different types of distortions present in such lines. How can these distortions be avoided?



14.a) Describe the losses in transmission lines. b) Derive the characteristic impedance of a transmission line in terms of its line constants.

Part B: Model Problems* A load Impedance of 90-j25 Ω is to be matched to a 50Ω line using single stub matching. Find the length and position of the stub.

* A transmission line is terminated in a load Impedance ZL = 73+j42.5 Ω, the frequency = 107 Hz line length l = 10 m. The inductance L = 10-6 H/m C=1/9X 10-10 F/m. Find ZL?

* A lossless TX line has 75 ohms characteristic impedance. The line is terminated in a load impedance of (50-j100) ohms. The maximum voltage measured on the line is 100volts. Find the maximum and minimum current and minimum voltage on the line. At what distance from the load, the voltage and current are maximum.



* A line with Z0 = 100Ω is connected to an impedance (load) ZL = 300 + j200. Find i. the line length ‘d1’ required to transform this load to a pure resistance

ii. the impedance of a λ/4 line required for a match iii. VSWR on the `d1' line and VSWR on λ/4 line. Use Smith chart.

* An antenna of 76 Ω is to be matched to a loss less line of 50(=Z0)Ω. Explain the procedure.

* A TX line has primary constants R = 0.1Ω/mt, G = 0.01 mhos/mt, L =0.01µH/mt; C = 100PF/mt. If the line is connected to a load impedance of (10+J20) ohms, find reflection coefficient at the i. load endii. 20 cm from load.

* Given R=10.4 ohms/mile; L=.00367 H/mile, G = 0.8 X10-6 mho/mile; C=0.00835 µF/mile. Evaluate α,β,γ, Z0, v at 1 KHZ.



* A 30m long lossless transmission line with Z0 = 50Ω operating at 2.0 MHz is terminated by a load ZL = 60 + j40 Ω on the line. Find

i. the reflection coefficientii. the VSWR and the input impedance.

Velocity of signal on the line is v = 0.6c(c = velocity in free space)(use smith's chart)

* A 50.0 ohm Coaxial line feeds a 75 + j20 Antenna. Find Reflection Coefficient and VSWR.

* A transmission line operating at ω = 106 rad/s has α= 8 db/m; β = 1 rad/m and Z0 = 60 + j 40 Ω and is 2.0 m long. If the line is connected to a source of 10.0 ∟ 00 volts, Zg = 40Ω(source) and is terminated by a load ZL = 20 + j50 Ω. Determine i. the input impedance ii. the sending end current iii. the voltage at the load end.

* A 50 mt line has the following measurements made, at 1200 Hz. ZinOC = 200 ∟-420 ohms; ZinSC = 1890∟220

ohms. Find Z0 α,β and v for the line.



* Given R = 10.4 Ω/mt; L = 0.00367 H/mt; G = 0.8 x 10-4 mhos/mt; C = 0.00835 µF/mt. Calculate Z0 and γ at 1.0 KHz.

* An antenna with Radiation resistance of ZL = 73 Ω is to be matched to a lossless line of Z0 = 50 ohms. Evaluate a simple matching mechanism to match the antenna to the line. Give the values.

* A lossless TX line has 75 ohms characteristic impedance. The line is terminated in a load impedance of (50- J100) ohms. The maximum voltage measured on the line is 100volts. Find the maximum and minimum current and minimum voltage on the line. At what distance from the load, the voltage and current are maximum.

* A load has admittance YL/Y0= = 1.25 + j0.25. Find the length and location of a single stub to match the line to the load use Smith chart.

* The propagation constant of a lossy transmission line is 1+2j m-1 and its characteristic impedance is 20+j 0Ω at

ω= m rad/sec. Find L,C,R & G for the line.



* A Lossless line is having Z 0 = 120 Ω is operating at ω= 5 x 10 8 rad/sec. If the velocity on the line is 2.4x108 m/s find L & C. Let ZL be represented by an inductance of 0.6µH in series with a 100Ω resistance. Find reflection coefficient and VSWR.

*A 50 ohm transmission line operates at 10 MHz, with a velocity of 2x108m/s. If the load impedance is 60 + j10 ohms, determine its input impedance for a line length of 10m and 5m.

* A 60 ohm lossless line is 30m long and terminated with a load of 75+ j 50 ohms at 3 MHz. Find its reflection coefficient , VSWR, ZMAX and ZMIN, if the velocity is 60 % of the velocity of light.

Part C: Short Answer Questions1.Define the line parameters?

2. What are the secondary constants of a line? Why the line parameters are called distributed elements?

3.Define Characteristic impedance



4. Define Propagation constant

5.What is a finite line? Write down the significance of this line?

6.What is an infinite line?

7.What is wavelength of a line?

8.What are the types of line distortions?

9.How frequency distortion occurs in a line?

10.How to avoid the frequency distortion that occurs in the line?

11.What is delay distortion?



12. How to avoid the frequency distortion that occurs in the line?

13.What is a distortion less line? What is the condition for a distortion less line?

14.What is the drawback of using ordinary telephone cables?

15.How the telephone line can be made a distortion less line?

16.What is Loading?

17.What are the types of loading?

18.What is continuous loading?

19.What is patch loading?

20.What is lumped loading?



21.Define reflection coefficient

22. Define reflection loss

23.What is Impedance matching?

24. Define the term insertion loss

25.When reflection occurs in a line?

26.What are the conditions for a perfect line? What is a smooth line?

27.State the expressions for the capacitance of a open wire line

28.What is standing wave ratio?



29.What is the range of values of standing wave ratio?

30.State the relation between standing wave ratio and reflection coefficient.

31.What are standing waves?

32. Bring out the significance of a half wavelength line.

33. Give some of the impendence –matching devices.

34. Explain impendence matching using stub.

35.Give reasons for preferring a short- circuited stub when compared to an open circuited stub.

36.What are the two independent measurements that must be made to find the location and length of the stub.



37. List the applications of the smith chart.

38. What are the difficulties in single stub matching?

39. What is double stub matching?

40. Give reason for an open line not frequently employed for impedance matching.

41. State the use of half wave line .

42. Why Double stub matching is preferred over single stub matching.


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EMTL 4 Units Important Questions