Here is the systematically categorized question bank for ECE 2105: Electromagnetic Fields and Waves, compiled from the provided 2015-2025 exam papers.
As requested, questions are strictly categorized, reproduced verbatim without truncation, and grouped only if the wording is identical (accounting for minor typographical variations in the source papers).
Topic 1: Vector Calculus & Electromagnetic Fundamentals
| Subtopic | Exact Question + [Marks] | Year(s) of Appearance |
|---|---|---|
| Field Concept & Necessity | What are the inadequacy of circuit-theory concepts and why we need electromagnetic field concept? Explain the physical significance of divergence in terms of electromagnetic field. (05+02) | 2018 |
| Show the inadequacy of circuit theory concept and necessity of electromagnetic field concept with two examples. Define metric coefficient. (08+02) | 2019 | |
| Point out the inadequacy of the circuit-theory and explain the necessity of electromagnetic field concept with necessary examples. (08) | 2021 | |
| Explain the meaning of word ‘field’ in terms of electromagnetics. Elucidate the significance of studying electromagnetic fields and waves as an Electronics and Communication Engineer. (10) | 2024 | |
| What is implied by “quasi-static conditions” in electromagnetics. (05) | 2020 | |
| Vector Calculus (Curl & Div) | Write down the properties of curl operation. What are the consequences of a vector being curl free? (05+02) | 2022 |
| Let, (Wb/m) in a certain region of free space. i) Find . ii) Find , and at P(3, -1, 2). (12/10) | 2022, 2025 | |
| Media Properties | Define homogeneous, linear and isotropic media. (06) | 2015, 2017, 2023, 2024 |
| Write short description on the conditions when a same medium can be act as a good conductor or a good insulator. (10) | 2020 | |
| Write short notes on (i) loss tangent (ii) homogenous medium (iii) complex permittivity. (09) | 2019 | |
| Briefly discuss the following terms: i) Intrinsic impedance, ii) Complex permittivity, iii) Displacement current density. (09) | 2023 | |
| Briefly explain the following terms: i) Intrinsic impedance ii) Virtual height. (06) | 2022 |
Topic 2: Electrostatics
| Subtopic | Exact Question + [Marks] | Year(s) of Appearance |
|---|---|---|
| Fundamental Postulates | Write and explain the differential form of the fundamental postulates of electrostatics in free space. Also explain the integral form of fundamental postulates. (10) | 2015 |
| Write down the fundamental postulates of electrostatics in free space in both differential and integral form and also write down their physical significance. (08) | 2016 | |
| Write down the differential and integral form of fundamental postulates of electrostatics in free space and also state their physical significance. (08) | 2017 | |
| Write down the differential form of fundamental postulates of electrostatics in free space. Then derive the integral form of them. Also state their physical significance. (10) | 2020, 2022 | |
| Explain the fundamental postulates of electrostatics in free space in both their differential and integral forms. State their physical significance. (10) | 2025 | |
| Coulomb’s Law | State Coulomb’s law. Explain electric field intensity due to a continuous distribution of charge with (i) surface charge density and (ii) line charge density. (10) | 2021 |
| State Coulomb’s law. Determine the electric field intensity due to a continuous distribution of charge with (i) surface charge density and (ii) line charge density. (10) | 2018 | |
| Electric Field & Potential Theory | Define electric field intensity and electric potential. Also derive the relation between them when caused by a point charge. (10) | 2016 |
| Define electric potential. Show that in an electric filed, work done in moving a unit charge from one point to another is equal to the electric potential difference between that two points. (08) | 2017 | |
| Define electric potential and state the relation between electric potential and electric field intensity. (06) | 2021 | |
| Differentiate between electric field intensity and electric flux density, emphasizing their physical significance. (05) | 2022 | |
| Distinguish between electric field intensity and electric flux density with respect to definition, unit, governing relation, and physical significance. (07) | 2025 | |
| Define equipotential line. Draw the electric field lines and the equipotential lines of a uniform charge sphere. (07) | 2024 | |
| Make a two-dimensional sketch of the electric field lines and the equipotential lines of a uniform charge sphere and a dipole. Ensure the lines are distinguishable. (10) | 2025 | |
| Gauss’s Law & Applications | State and explain Gauss’s law. Using this law, determine the electric field intensity of sheet charge. (11) | 2015 |
| State and explain Gauss’s law. Using this law determine electric field intensity and electric potential of an infinitely long straight line charge of a uniform density in air. (12) | 2016 | |
| State and explain Gauss’s law. Using this law, determine the electric field intensity of an infinite sheet of charge. (10) | 2023 | |
| State Gauss’s law and also write some applications of it. (05) | 2019 | |
| Write down some applications of Gauss’s law. Show that the electric field intensity inside a uniformly charged varies linearly up to the surface and varies inversely outside of the charged cloud. (20) | 2020 | |
| Show that the strength of the electric field intensity due to the field of a charge cloud is maximum at the surface of that charge cloud. (12) | 2019 | |
| Show that the electric field intensity inside a uniformly charged cloud is zero at it’s centre and varies linearly upto the surface. (09) | 2018 | |
| Show that electric field intensity inside a uniformly charged cloud is zero at its center and varies linearly up to the surface. (10) | 2022 | |
| Electric Dipole | Define electric dipole moment. Deduce the electric field intensity of an electric dipole in terms of its dipole moment. (13/10) | 2016, 2023 |
| Define electric dipole moment. Estimate the electric potential (V) at any P point in space due to an electric dipole, assuming the distance of the point P is far greater that the distance between the charges. (12) | 2021 | |
| Define electric dipole. Derive the equation of electric potential due to an electric dipole and explain how electric potential varies with distance and angle of position. (13) | 2019 | |
| Two equal charges, q of opposite sign, separated by a distance ‘l’ constitute an electric dipole. Derive an expression for the electric dipole (V) at P point in space due to this dipole, assume that the point is not too close to the dipole. (12) | 2017 | |
| Two equal but opposite charges separated by a distance, l constitute an electric dipole. Derive an expression of the electric potential at an arbitrary point P in space due to this dipole assuming P is not too close to the dipole. (12) | 2024 | |
| Dielectrics & Boundary Conditions | Show that the total electric flux density in a dielectric material is , where the symbols have their usual meanings. (07/08) | 2016, 2019, 2021 |
| Consider a plane boundary between two dielectric media (with zero conductivities) and establishes a relationship between the tangential and normal components of the electric field on both sides. What happens when one of the media is a conductor? (07) | 2015 | |
| Determine the normal and tangential components of electric field intensity , and electric flux density, at the boundary of a conductor and free space. (09) | 2016, 2020 | |
| Two dielectric media with permittivities and are separated by a charge-free boundary as shown in Fig. 1(d) [or Fig. 2(b) or Fig. 3(a)]. The electric field intensity in medium 1 at the point has a magnitude and makes an angle with the normal. Determine the magnitude and direction of the electric field intensity at point in medium-2. (08/09) [Figure provided] | 2017, 2019, 2022 | |
| Two dielectric media having permittivities and are separated by a charge free boundary. An electric field in medium 1 makes an angle with the normal. Derive the boundary conditions and determine the magnitude and direction of the electric field in medium 2. (08) | 2025 | |
| Capacitance & Laplace/Poisson | Deduce the equations of Poisson’s and Laplace expressing the relationship of the space rate of variation of electric field component with the distributed charge field. (08) | 2015 |
| Write down the Laplace and Poisson’s equation. Using Laplace equation find out the capacitance of a parallel plate capacitor as shown in Fig. 2(c). (10) [Figure Q. 2(c)] | 2016 | |
| Derive the Poisson’s equations with respect to an electric potential. What will be the solution of it? (08/11) | 2017, 2023 | |
| Derive the Poisson’s equation for electrostatics. (08/05) | 2022, 2025 | |
| A parallel plate capacitor consists of two plates with a separation d in between plates. The space between the conductors is filled with a dielectric of permittivity and the surface area of capacitor plates is A, determine the capacitance of this capacitor. (12/13) | 2018, 2019, 2023, 2024 | |
| A parallel plate capacitor consists of two plates with a separation d in between plates. The space between the conductors in field with a dielectric of permittivity and the surface area of capacitor plates is A, determine the capacitance of the capacitor. (13) | 2022 | |
| The two plates of a parallel plate capacitor are separated by a distance and maintained at potential 0 and , as shown in figure 4(b). Assuming negligible fringing effect at the edges, estimate the (i) potential at any point between the plates, and (ii) surface charge density on the plates. (11) [Figure 4(b)] | 2021 | |
| A fixed voltage is applied across a parallel plate capacitor separated by a distance d. assuming negligible fringing effect, determine the surface charge density on each of the plates. (11/12) | 2022, 2025 | |
| A cylindrical capacitor consists of an inner conductor of radius ‘a’ and outer conductor whose inner radius is ‘b’. The space between the conductors is filled with a dielectric of permittivity , and the length of the capacitor is L (or l). Determine the capacitance of this capacitor. (10/13) | 2015, 2017 | |
| Electrostatic Energy | What is electrostatic energy? Derive an equation for electrostatic energy to assemble k charges one by one. (12) | 2018, 2022 |
| Define electrostatic energy. Determine the electrostatic energy for assembling k charges one by one. (12) | 2023 | |
| Define electrostatic energy. Derive the expression of electrostatic energy for a system of direct charges. (12) | 2024 | |
| Define electrostatic potential energy. Derive the expression for the work done in assembly n point charges one after another from infinity. (13) | 2025 | |
| Electric Field Math Problems | A negative point charge of magnitude is situated in air at origin and two positive point charges of each are at points y=2 meters. Calculate the electric field strength and electric potential at a point 4 meters from the origin on the x axis. (09/10) | 2016, 2018 |
| A positive point charge of magnitude is situated in air at the origin of a rectangular co-ordinate system. Calculate the electric field strength at a point on the z-axis 8 meters from the origin. (07) | 2017 | |
| A spherical uniform charge distribution in free space has nC/m for and zero otherwise. Calculate at r = 2m and r = 12m; where the symbols have their usual meanings. (10) | 2021 | |
| What is the potential at the centre of a rectangular whose side a=2.0 metre, b=1.0 metre, and charges , and are respectively C, C, C, and C. Follow the figure 2(c). (10) [Figure Q.2(c)] | 2020 | |
| What is electrostatic energy? What energy is stored in the field with point charges 1, -2, -3 and 4 C are located on the x-axis at x= 1,2,3,4 meter respectively? (10) | 2019 | |
| What is electrostatic energy? Calculate the energy stored in the field with point charges -2, 1, 3, and -4 C are located on the x-axis at x= 1, 2, 3, 4 meters respectively. (10) | 2020 | |
| What energy is stored in the field with point charges 1, -2, -3, and 4 C are located on the X-axis at x = 1, 2, 3, 4 meter respectively. (08) | 2023 | |
| Determine the work done in carrying a -2C charge from to in the field, along the straight line joining and . (12) | 2022, 2025 | |
| In an electrohydrodynamic pump, the region as shown in Fig. 2(b) between the two electrodes is filled with a uniform charge density . If the left electrode has a potential of and the right electrode has a potential of 0 V, determine the expressions for electric potential and electric field intensity at any point between the electrodes. (13) [Figure 2(b)] | 2024 | |
| A positive point charge Q is at the center of a spherical conducting shell of an inner radius and outer radius . Illustrate the variation of electric field intensity and electric potential V, as a function radial distance R. (12) | 2025 |
Topic 3: Magnetostatics
| Subtopic | Exact Question + [Marks] | Year(s) of Appearance |
|---|---|---|
| Biot-Savart Law & Applications | Derive the equation for Biot-Savart law. Point out the application of Biot-Savart law in magnetostatics. (09) | 2021 |
| Derive the equation for Biot-Savart law. Point out the application of Biot-Savart law in comparison to Ampere’s circuital law. (12) | 2024 | |
| A direct current I flows in a straight wire of length L. Find the magnetic flux density at a point located at a distance r from the wire in the bisecting plane. (15) | 2015 | |
| A direct current I in figure 6(b) [or Fig 5(b)] flows in a straight wire of length 2L. Find the magnetic flux density B at a point located at a distance ‘r’ from the wire in the bisecting plane; (i) by determining the vector magnetic potential A first, and (ii) by applying Biot-Savart law. (15/18) [Figure Provided] | 2016, 2021 | |
| A direct current I follows in a straight wire of length 2L. Find the magnetic flux density B at a point located at a distance r from the wire in the bisecting plane by applying Biot-Savart law. (10) [Figure 7(a)] | 2023 | |
| A direct current I flows a straight wire of length 2L. Find the magnetic flux density B at a point located at a distance r from the wire in the bisecting place by determining the vector magnetic potential A. (12) | 2025 | |
| State and explain Bio-Savart law. With the help of this law, find the magnetic flux density at the center of a square loop with side w carrying a direct current I as shown in Fig. 5(b). (12) [Fig. 5(b)] | 2017 | |
| Ampere’s Law & Comparisons | State and explain Ampere’s circuital law. (02) | 2016 |
| State and explain Ampere’s circuital law. Also, write down Lorentz force equation. (10) | 2021 | |
| State and explain Ampere’s circuital law and Biot-Savart law. Also compare the usefulness/importance of these laws in determining magnetic flux density. (10) | 2015, 2018, 2023, 2025 | |
| State and explain Ampere’s circuital law. Suppose an infinity long straight conductor with a circular cross-section of radius b carries a steady current I. Determine the magnetic flux density both inside and outside the conductor. (11) | 2017 | |
| An infinitely long, straight conductor with a circular cross section of radius b carries a steady current I. Determine the magnetic flux density both inside and outside the conductor. (10) | 2022 | |
| Write down the Lorentz’s force equation. An infinite long, straight conductor with a circular cross section of radius b carries a steady current I. Determine magnetic flux density both inside and outside of the conductor. (02+11) | 2018 | |
| Vector Magnetic Potential | State the law of conservation of magnetic flux. Deduce vector Poisson’s equation and hence find the vector magnetic potential from it. (04+08) | 2020 |
| What is vector magnetic potential. Show that line integral of any vector magnetic potential around any closed path equals the total magnetic flux passing around the area enclosed by the path. (02+06) | 2019 | |
| What is vector magnitude potential? Derive the expression of vector magnetic potential. (12) | 2024 | |
| Distinguish between vector magnetic potential and scalar magnetic potential. (05/10) | 2015, 2019 | |
| An infinite long, straight conductor with a circular cross section of radius ‘b’ carries a steady current ‘I’. Determine vector magnetic potential ‘A’ both inside and outside of the conductor. (13) | 2020 | |
| Magnetic Dipole & Magnetization | Define magnetic dipole. How do you calculate magnetic dipole moment? What are the dissimilarities between electric dipole and magnetic dipole? (13) | 2015 |
| Define magnetic dipole. How do you calculate magnetic dipole moment? (06) | 2017 | |
| What are the dissimilarities between electric dipole and magnetic dipole. (07) | 2017 | |
| Find the magnetic flux density at a distant point of a small circular loop of radius b that carries current I in terms of dipole moment. (10/12/14/15) [Figure Provided in some years] | 2015, 2016, 2017, 2018, 2019, 2021, 2022, 2025 | |
| Define magnetization vector. Relate this parameter with equivalent current and charge densities. (10) | 2015 | |
| Briefly explain magnetization vectors. Show that volume current density and surface current density are expressed as (A/m) and (A/m) respectively, where the symbols have their usual meanings in electromagnetics. (11) | 2016 | |
| Show that the volume current density and surface current density are expressed as and respectively. where the symbols have their usual meanings in electromagnetics. (10) | 2018, 2022, 2025 | |
| ”A magnetized body may be replaced by an equivalent magnetization surface charge density and an equivalent magnetization volume charge density”-justify the statement. (10) | 2017 | |
| A cylindrical bar magnet of radius b and length L has a uniform magnetization along its axis as shown in Fig. 6(c) [or Fig 6(b)]. Use the equivalent charge density concept to determine the magnetic flux density at an arbitrary distant point. (11/16) [Figure Provided] | 2016, 2019 | |
| Determine the magnetic flux density on the axis of a uniformly magnetized circular cylinder of a magnetic material. The cylinder has a radius b, length L, and axial magnetization . (10/12) | 2021, 2024 | |
| ”Magnetic poles cannot be isolated”- justify the statement. (08) | 2025 | |
| Magnetic Boundary Conditions | Show that the normal component of B is continuous across an interface and tangential component of H is continuous across the boundary of almost all physical media, where the symbols have their usual meanings in electromagnetics. (08) | 2019 |
| Explain how the magnetic field varies at the interface between two different medium with proper illustration. (06) | 2022 | |
| Mention the boundary conditions at an interface between magnetic medium and air. Also calculate magnetic field intensity at an arbitrary point on the interface between these two media. (12/13) | 2015, 2023 | |
| Mention the boundary conditions at an interface between a magnetic medium and air. Also, prove that the tangential component of H field is discontinues across an interface where a free surface current exists. (13) | 2025 | |
| What are the boundary conditions for magnetostatic fields at an interface between two magnetic media? Suppose two magnetic media with permeabilities and have a common boundary as shown in Fig. 7(a). The magnetic field intensity in medium 1 at the point P has a magnitude and makes an angle with the normal. Determine the magnitude and the direction of the magnetic field intensity at point in medium 2. (14) [Fig. of Q. 7(a)] | 2016, 2024 | |
| What are the boundary conditions for magnetostatic field at the interface between two medium? For the following figure (Fig. 5(b)), if , and then find (12) [Figure 5(b)] | 2023 | |
| In the figure 6(d) [or 8(b)] if , and then find . (05/09) [Figure Provided] | 2018, 2021 | |
| Consider a plane boundary (y=0) between air (region 1, ) and Iron (region 2, ). (i) Assuming : Find and the angle that makes with the interface. (ii) Assuming , find and the angle that makes with the normal to the interface. (10/12) | 2017, 2023 | |
| Magnetic Forces & Energy | Determine the force per unit length between two infinitely long parallel conducting wires carrying currents and in the same direction, separated by a distance d as shown in Fig. 8(b). (08/10) [Figure Provided] | 2017, 2022, 2024 |
| Discuss the forces between two parallel current-carrying conductors, explaining their magnitude, direction, and the conditions under which they attract or repel each other. (15) | 2025 | |
| ”Forces on current carrying conductor holds the Newton’s third law”- Identify whether this statement is true or false and also explain the reason behind it with necessary equation. (11/12/14) | 2018, 2020, 2023 | |
| Derive the expression for the torque experienced by a rectangular current carrying loop placed within a uniform magnetic field. (08) | 2022 | |
| Derive the expression for the magnetic energy of a system of N current carrying loops. (10/12) | 2022, 2024 | |
| Derive/Deduce the expression of total magnetic energy that can be obtained from two mutually coupled circuits. (13/16) | 2019, 2020 | |
| Consider two closed loops and carrying current and respectively. Find the expression of energy stored in the magnetic field. Also show that Newton’s third law holds here. (17) | 2015 | |
| Demonstrate the analogous relation between the quantities in electrostatics and those in magnetostatics. (06/07) | 2021, 2023 | |
| Demonstrate the analogous relation between the quantities in electrostatics and those in magnetostatics. Deduce the equation of energy stored in magnetic field. (04+06) | 2018 | |
| Deduce the equation of energy stored in magnetic field. (07) | 2023 | |
| Hall Effect & Short Notes | Explain the Hall effect with appropriate figure. Also derive the expression for Hall voltage. (13) | 2025 |
| Explain ‘hall effect’ with appropriate figure. (05/06) | 2019, 2021 | |
| Write short notes on: i) vector magnetic potential ii) magnetic susceptibility. (06) | 2022 | |
| What is the role of magnetic susceptibility? Explain briefly. (12) | 2015 | |
| Briefly explain the following terms: i) Vector magnetic potential, ii) Magnetic Susceptibility iii) Skin depth. (12) | 2025 | |
| Explain the following terms: i) Vector magnetic potential, ii) magnetic dipole moment, iii) magnetic field intensity. (09/12) | 2016, 2018 |
Topic 4: Time-Varying Fields & Maxwell’s Equations
| Subtopic | Exact Question + [Marks] | Year(s) of Appearance |
|---|---|---|
| Continuity Eq & Conservation | State the principle of conservation of charge. Based on this principle, derive the continuity equation, , where the symbols have their usual meanings. Also write down the physical significance of this equation. (09/10) | 2015, 2018, 2022 |
| State the principle of conservation of charge. Through this principle, deduce the continuity equation, , where the symbols have their usual meanings. Also, write down the physical significance of this equation. (10) | 2019 | |
| State the principle of conservation of charge. Explain how this principle can extend to continuity equation and the significance of the equation. (10) | 2021 | |
| Explain the law of conservation of charge. Starting from this law, derive the continuity equation. . Where the symbols have their usual meanings. Briefly discuss its physical interpretation. (10) | 2025 | |
| Derive and explain the continuity equation along with its significance. (08) | 2024 | |
| Maxwell’s Equations | Write down the differential and integral form of Maxwell’s equations with their physical significance. (08/09/10) | 2015, 2021, 2023, 2024, 2025 |
| Write down the differential form and integral form of the Maxwell’s equations and identify each equation with proper experimental law. (07/08) | 2016, 2017 | |
| Deduce Maxwell’s equations from the four fundamental governing equations of electrostatics and magnetostatics. (08/13) | 2018, 2023 | |
| Derive Maxwell’s equation from fundamental electrostatic and magnetostatic expressions by incorporating Faraday’s law of electromagnetic induction and continuity equation. (10) | 2019 | |
| Write down the significance of Maxwell’s equations. (05) | 2018 | |
| Boundary Conditions (Dynamic) | Why the boundary conditions for electromagnetic fields are same to the boundary conditions for static electric and static magnetic field. (10) | 2020 |
| Write down the boundary equations for both electric field vectors and magnetic field vectors. Hence derive (i) boundary conditions between two lossless media and (ii) boundary conditions between a dielectric media and perfect conductor. (08/09/10) | 2018, 2021, 2022, 2023, 2024 | |
| Write down the boundary conditions between two electromagnetic medium. (06) | 2019 | |
| Displacement Current & Power Flow | Define displacement current. Determine the displacement current in between two parallel plates of a capacitor energized by an alternating current source. (07/09) | 2016, 2017 |
| State and explain Poynting’s theorem. (09) | 2015 | |
| State and explain Poynting’s theorem with necessary equations. Also denotes the pointing vector . (10) | 2023 | |
| Find the equation of the total power flowing in a closed surface due to electromagnetic waves at any instant. (10/13) | 2016, 2022, 2024 | |
| Find the Poynting vector on the surface of a long straight conducting wire (of radius b and conductivity ) that carries a direct current I as shown in Fig. 8(b). Also verify Poynting’s theorem. (08) [Fig. 8(b)] | 2017 |
Topic 5: Electromagnetic Waves
| Subtopic | Exact Question + [Marks] | Year(s) of Appearance |
|---|---|---|
| Wave Equations | Deduce the homogeneous wave equations for both scalar and vector potentials. How would these equations turn out to be non-homogeneous? (12) | 2015 |
| Deduce the homogeneous wave equations for both scalar and vector potentials. (10/13) | 2017, 2022, 2023, 2025 | |
| Explain scalar and vector potentials along with their significances. Deduce the homogeneous wave equations for both potentials. (13) | 2024 | |
| Write and analyze the homogeneous wave equation for both scalar and vector potentials. Explain how these equations would turn out to be nonhomogeneous. (10) | 2021 | |
| Using Lorentz’s gauge deduce the nonhomogeneous wave equation for vector potential and scalar potential V. (12) | 2016 | |
| Derive the general wave equation for and and convert them to Helmholtz’s equations for sinusoidal time dependence. (13) | 2025 | |
| Starting from Maxwell’s equations obtain homogeneous vector Helmholtz’s equation. (10) | 2016 | |
| State the homogeneous vector Helmholtz’s equation and explain the term ‘wave number’. (05) | 2021 | |
| Write and explain the significance of the Helmholtz’s equation. (06) | 2023 | |
| Write the form of Helmholtz’s equation in long medias. (05) | 2018 | |
| Show that using Maxwell’s equation. (08) | 2018 | |
| Show that the electromagnetic field vector travels with speed through the derivation of homogeneous vector wave equation for source free fields in simple media. (10) | 2019, 2024 | |
| Deduce the fundamental equation for free space propagation. (08/11) | 2017, 2021 | |
| Show that if and are solutions of source free Maxwell’s equation in simple medium characterized by and , then so also and , where ; ; Where . (10) | 2024, 2025 | |
| Starting from homogeneous wave equation, show that the scalar potential at a distance from the surface at time t depends on the value of the charge density at an earlier time . (12) | 2018 | |
| Wave Propagation (Lossy & Lossless) | Determine: (i) attenuation constant and (ii) phase constant for both low-loss dielectrics and good conductor. (12/13) | 2019, 2025 |
| Explain low loss dielectrics and good conductors with your knowledge of electromagnetics. (09/12) | 2017, 2023 | |
| What do you mean by loss tangent? Discuss the characteristics of i) good conductor, ii) lossy dielectric and iii) skin depth. (12) | 2015 | |
| Define phase velocity and group velocity of a plane wave, and explain the concept of dispersion in wave propagation. (10) | 2024 | |
| Investigate why there will be no dispersion when group velocity and phase velocity are equal. Prove that . (03+08) | 2018 | |
| Propagation Math Problems | A uniform plane wave with, propagates in a lossless simple medium () in the +z direction. Assume that is sinusoidal with a frequency 100 MHz and has a maximum magnitude of (V/m) at t=0 and z=1/8 (m). (i) Write the instantaneous expression for in any t and z. (ii) Write the instantaneous expression for . (08) | 2021 |
| A uniform plane wave with propagates in a lossless simple medium () in the direction. Assume that is sinusoidal with a frequency 150 MHz and has a maximum value of at t = 0 and . (i) Write the instantaneous expression for E for any t and z, (ii) Write the instantaneous expression for H, (iii) Determine the location where is a positive maximum when . (15) | 2019 | |
| The electric field intensity of a linearly polarized uniform plane wave propagating in the +z direction in sea water is (V/m) at z = 0. For sea water and (s/m). Determine: i) the attenuation constant, phase constant, intrinsic impedance, phase velocity, wavelength and skin depth, and ii) the distance at which amplitude in 1% of its value at z = 0. (14/15) | 2018, 2024 | |
| A narrow band signal propagates in a lossy dielectric medium which has a loss tangent 0.2 [or 0.3] at 550 KHz [or 530 KHz], the carrier frequency of the signal. The dielectric constant of the medium is 2.5; (i) Determine and . (ii) Determine and . Is the medium dispersive? (10/11/12) | 2017, 2019, 2021 | |
| A sinusoidal electric intensity of amplitude 250(V/m) and frequency 1GHz exists in a lossy dielectric medium that has a relative permittivity of 2.5 and a loss tangent of 0.001. Find the average power dissipated in the medium per cubic meter [or per cube]. (08/09/10) | 2017, 2022, 2023, 2024 | |
| A y-polarized uniform plane wave () with a frequency of 100 MHz propagates in air in the +x direction and impinges normally on a perfectly conducting plane at x=0. Assuming the amplitude of to be 6 mV/m, write the phasor and instantaneous expression for a) and of the incident wave; b) and of the reflected wave, and c) and of the total wave in air, d) Determine the location nearest to the conducting plane where is zero. (08/19) | 2015, 2016 | |
| Reflection, Transmission & Polarization | If an EM wave follows normal incidence at a plain dielectric boundary, show that the reflection coefficient, and the transmission coefficient, are related by . (10/11/12/13/14/15) | 2015, 2016, 2017, 2019, 2021, 2022, 2023, 2024 |
| What is meant by polarization of a wave? Two orthogonal linearly polarized waves are combined. State the conditions under which resultant will be (i) another linearly polarized wave, (ii) a circularly polarized wave, and (iii) an elliptically polarized wave. (11/12/13) | 2016, 2021, 2023, 2024, 2025 | |
| ”Superposition of two linearly polarized waves: one polarized in x direction and the other in the y direction and leading [or lagging] by with equal [or different] amplitude gives rise to negative circularly polarized wave” - justify the statement. (11/13/15) | 2018, 2021, 2022 | |
| What is meant by polarization of a wave prove that a linearly polarized plane wave can be resolved into a right hand circularly polarized wave and a left hand circularly polarized wave of equal amplitude. (08) | 2017 | |
| Upon what condition a wave is said to be i) elliptically polarized? ii) circularly polarized? (09) | 2015 | |
| Mathematically prove that in case of non-magnetic media, Brewster’s angle exists only for parallel polarizations rather than for perpendicular polarizations. (13) | 2022 | |
| Define Brewster angle. (04) | 2020 | |
| Why standing wave is created when a plane electromagnetic wave incident normally on a plane conducting boundary? Explain it with necessary equation. (02+08/10) | 2018, 2020 | |
| Explain Doppler effect in electromagnetics with proper illustration. How does the Doppler effect relate to the red-shift of a receding star? (13) | 2024 | |
| Explain Doppler effect with proper mathematical illustration. (07/10) | 2015, 2017, 2019 | |
| Which effect causes the ‘red shift’ of the light spectrum emitted by a receding distant star. State two more practical examples of this particular effect. (06) | 2020 |
Topic 6: Radio Wave Propagation
| Subtopic | Exact Question + [Marks] | Year(s) of Appearance |
|---|---|---|
| Propagation Modes | State the mode of propagation for each of the following services and explain the reason (i) SW radio Broadcasting (ii) Cellular Telephones (iii) Satellite Communication. (06/09/10) | 2015, 2019, 2021, 2022 |
| What are the different types of propagation of radio waves from the radiating antenna to the receiving antenna? Explain with their practical examples. (10/12) | 2017, 2018, 2023 | |
| Explain line of sight communication mode. Determine the maximum distance between two antennas in case of line of sight communication. (06/11) | 2016, 2019 | |
| A VHF communication is to be established with 35W transmitter at 90 MHz. Find the distance up to which line of sight communication may be possible if the height of the transmitting and receiving antennas are 40m and 25m respectively. Also, determine the field strength at the receiving end. (12) | 2017 | |
| Why ground wave propagation is not suitable for more than 2 MHz? Also explain the effects of earth’s curvature on radio wave propagation. (08) | 2016 | |
| Ionospheric Terms & Frequencies | Define i) Virtual height, ii) skip distance, iii) maximum usable frequency (MUF)- as used in radio wave propagation. (06) | 2015, 2016, 2018 |
| What is meant by virtual height in wave propagation? Why virtual height is used rather than actual height? (07/08) | 2018, 2020, 2021 | |
| Define plasma frequency. Why standing wave is created when a plane electromagnetic wave incident normally on a plane conducting boundary. Explain it with necessary equation. (02+08) | 2018 | |
| Derive the equation of plasma frequency of ionized medium. If total number of electrons in the ionosphere is around per cm, then what is the minimum frequency above which radio communication can be established between space-craft and earth? (07/10) | 2019, 2023 | |
| A high frequency radio link has to be established between two points at a distance of 250 km on earth’s surface. Considering the ionospheric height to be 200 km and it’s critical frequency 5 MHz, calculate the maximum usable frequency (MUF) for the given path. (10) | 2018 | |
| Two points on earth are 1500 Km apart, and are to communicate by means of HF. For a single hop transmission, the critical frequency at that time is 7 MHz and conditions are idealized. Calculate the MUF for those two points if the height of the ionosphere layer is 300Km. (08) | 2019 | |
| Explain the following terms: (i) Doppler effect, (ii) Skin depth and (iii) Plasma frequency. (09/10) | 2016, 2021 | |
| Given the skin depth for graphibet at 100 (MHz) is 0.20 (mm), determine (i) conductivity of graphite, and (ii) the distance that a 1 (GHz) wave travels in graphite such that its field intensity reduced by 30 dB. (10) | 2020 |