Speculative Questions

The following unsolved questions are based on the syllabus and recurring patterns in past technical examinations. Marks shown in brackets indicate the expected mark allocation. Past tags identify full subjective repeats; past component means the topic appeared within a composite question; related means an objective question or nearby wording supports the topic.

Vector Calculus and Field Operators

1. Define scalar field and vector field with electromagnetic examples. [5]

2. Explain why Cartesian, cylindrical and spherical coordinate systems are used in electromagnetic field problems. [5]

3. Define gradient, divergence and curl, and mention their physical meanings. [5]

4. State the divergence theorem and explain its use in deriving Gauss’s law in differential form. [5]

5. State Stokes’ theorem and explain its use in converting integral laws to differential form. [5]

6. What is curl? Explain its physical meaning in relation to circulation of a vector field. [5]

7. Distinguish between line, surface and volume integrals in electromagnetic field analysis. [5]

8. Derive the relation between closed-surface flux and divergence using the divergence theorem. [10]

Coulomb’s Law and Electric Field Intensity

1. State Coulomb’s law and define electric field intensity. [5]

2. Explain the principle of superposition for electric fields. [5]

3. Derive the electric field intensity due to a point charge. [5]

4. Write the electric field expression for a continuous charge distribution. [5]

5. Derive the electric field due to an infinite line charge. [10]

6. Derive the electric field due to an infinite sheet charge. [10]

7. Derive the electric field on the axis of a uniformly charged ring. [10]

8. Derive the electric field inside and outside a uniformly charged sphere. [10]

9. A point charge is placed in a dielectric medium. Find the electric field and force on another charge. [5]

10. Compare electric force and electric field intensity. [5]

Electric Flux Density, Gauss’s Law and Maxwell’s First Equation

1. Define electric flux density and electric flux. [5]

2. State Gauss’s law in integral and differential forms. [5]

3. Derive Maxwell’s first equation from Gauss’s law. [5]

4. Explain the physical meaning of $\nabla\cdot\mathbf{D}=\rho_v$. [5]

5. Apply Gauss’s law to find the field due to an infinite line charge. [10]

6. Apply Gauss’s law to find the field due to an infinite sheet charge. [10]

7. Apply Gauss’s law to find the field inside and outside a charged spherical shell or solid sphere. [10]

8. Explain how a Gaussian surface is selected for symmetric charge distributions. [5]

9. Compare the Coulomb-law and Gauss-law methods of field calculation. [5]

10. State the limitations of Gauss’s law as a calculation tool. [5]

Energy, Potential, Laplace and Poisson Equations

1. Define electric potential and potential difference. [5]

2. Derive $\mathbf{E}=-\nabla V$. [5]

3. Derive the potential due to a point charge. [5]

4. Explain equipotential surfaces and their relation to electric field lines. [5]

5. Derive electrostatic energy density. [5]

6. Derive the capacitance and stored-energy relation for a capacitor. [5]

7. Derive Poisson’s equation from Gauss’s law and the potential relation. [5]

8. Derive Laplace’s equation as a special case of Poisson’s equation. [5]

9. Solve the one-dimensional Laplace equation between two parallel plates. [10]

10. Explain boundary conditions at a conductor and dielectric interface. [10]

Magnetostatics, Magnetic Potential and Boundary Conditions

1. State the Biot–Savart law and explain each term. [5] (Related: NTC 2081/05/07 objective Q20)

2. Find the magnetic field intensity due to an infinitely long straight conductor. [5]

3. Find the magnetic field at the centre of a circular current loop. [5]

4. State Ampere’s circuital law and its differential form. [5]

5. Apply Ampere’s law to a long straight conductor, solenoid or toroid. [10]

6. Compare the Biot–Savart law and Ampere’s law. [5]

7. Define magnetic flux density and magnetic field intensity. [5]

8. Explain conduction current density and displacement current density. [5]

9. Distinguish between magnetic scalar potential and magnetic vector potential. [5] (Past: NTC 2081/05/07 Q2)

10. Derive the equation for magnetic vector potential. [10]

11. Derive magnetic boundary conditions at an interface. [10] (Past: NTC 2081/05/07 Q2)

12. State and explain all four electromagnetic boundary conditions. [10] (Related: NTC 2081/05/07 Q2)

13. Explain why the normal component of magnetic flux density is continuous at a boundary. [5]

14. Explain the boundary condition for tangential magnetic field intensity. [5]

15. State Maxwell’s equations in differential and integral forms, with their physical meanings. [10]

Free-Space Waves, Media and Skin Effect

1. Derive the wave equation for the electric field in a source-free lossless medium. [10]

2. Explain uniform plane-wave propagation in free space. [5]

3. Show that the electric field, magnetic field and direction of propagation are mutually perpendicular in a plane wave. [5]

4. Define intrinsic impedance and calculate its free-space value. [5]

5. Define phase constant, wavelength, frequency and phase velocity. [5]

6. Define the Poynting vector and explain its physical significance. [5]

7. Compare a perfect dielectric, lossy dielectric and good conductor. [5]

8. Define loss tangent and explain its significance. [5]

9. Explain attenuation and phase shift in a lossy medium. [5]

10. Derive skin depth for a good conductor. [10] (Related: NTC 2082/03/30 Q4)

11. Calculate skin depth for copper at a given frequency. [5] (Past component: NTC 2082/03/30 Q4)

12. Explain why skin effect is important in high-frequency communication systems. [5] (Past component: NTC 2082/03/30 Q4)

Transmission Lines and Impedance Matching

1. Draw the distributed-parameter model of a transmission line. [5]

2. Derive the telegrapher’s equations for a uniform transmission line. [10]

3. Define propagation constant and characteristic impedance. [5] (Past: CAAN 2076/08/22 Q13)

4. Derive characteristic impedance for a lossless line. [5]

5. Explain incident, reflected and standing waves. [5] (Related: NES 2082/12/11 Q6)

6. Define reflection coefficient and standing-wave ratio. [5] (Past: NTC 2075/05/23 Q2; CAAN 2076/08/22 Q13)

7. Explain how VSWR represents mismatch in a transmission line. [5] (Past: CAAN 2076/08/22 Q13)

8. Derive the input impedance of a lossless line. [10]

9. Explain a quarter-wave transformer and derive its matching condition. [10]

10. Compare quarter-wave transformer, single-stub matching and double-stub matching. [5]

11. A line of characteristic impedance $50\,\Omega$ is terminated by $100\,\Omega$. Find the reflection coefficient, VSWR and return loss. [5] (Related: NTC 2075/05/23 Q2; CAAN 2076/08/22 Q13)

12. Find the quarter-wave transformer impedance required to match a given real load. [5]

Antenna Fundamentals, Polarization and Dipole Radiation

1. Define an antenna and explain its transmitting and receiving functions. [5] (Past: CAAN 2074/07/25 Q7)

2. Define radiation pattern, beamwidth, directivity, gain, efficiency and effective aperture. [5]

3. Explain the near field and far field of an antenna. [5] (Past: CAAN 2074/07/25 Q7)

4. Write the expression for the far-field boundary and explain its significance. [5]

5. Mention types of antennas used in the VHF band. [5] (Past: NTC 2079/03/09 Q4)

6. How can the gain of a VHF antenna be increased? [5] (Past: NTC 2079/03/09 Q4)

7. Is a parabolic antenna feasible in the VHF band? Justify. [5] (Past: NTC 2079/03/09 Q4)

8. Draw and explain a Yagi–Uda antenna. [5] (Past: CAAN 2074/07/25 Q6; CAAN 2076/08/22 Q12)

9. Explain the working principle and applications of a Yagi antenna. [5] (Past: CAAN 2074/07/25 Q6; CAAN 2076/08/22 Q12)

10. Define polarization and explain linear, circular and elliptical polarization. [5] (Past: NTC 2075/05/23 Q2; past component: NTC 2082/03/30 Q4; related: NTC 2081/05/07 objective Q19)

11. Explain polarization mismatch and polarization loss factor. [5]

12. Discuss the working principle and radiation characteristics of a dipole antenna. [10] (Past component: NTC 2082/03/30 Q4)

13. Explain radiation resistance and directivity of a half-wave dipole. [5]

14. Compare a short dipole and half-wave dipole. [5]

15. Explain impedance matching in antenna systems. [5] (Past component: NTC 2082/03/30 Q4; related: NTC 2081/05/07 objective Q21)

Waveguides

1. Define a waveguide and state its use at high frequency. [5]

2. Compare a two-wire line, coaxial line and waveguide. [5]

3. Distinguish between TEM, TE and TM modes. [5]

4. Explain why a hollow rectangular waveguide cannot support TEM mode. [5]

5. Derive the cutoff frequency of a rectangular waveguide. [10]

6. Define the dominant mode and state the dominant mode of a rectangular waveguide. [5]

7. Calculate the cutoff frequency for the $\mathrm{TE}_{10}$ mode. [5]

8. Define guide wavelength, phase velocity and group velocity. [5]

9. Compare TE and TM wave impedances. [5]

10. Write short notes on resonant cavities. [5]

Mixed NTC-Style Questions

1. Discuss dipole radiation, polarization, impedance matching and skin depth with one numerical example. [10] (Past: NTC 2082/03/30 Q4)

2. Explain VHF antennas, methods of gain improvement and the feasibility of parabolic antennas in the VHF band. [10] (Past: NTC 2079/03/09 Q4)

3. Differentiate scalar and vector magnetic potentials and derive magnetic boundary conditions. [10] (Past: NTC 2081/05/07 Q2)

4. Explain characteristic impedance, reflection coefficient, VSWR and quarter-wave matching. [10] (Past components: NTC 2075/05/23 Q2; CAAN 2076/08/22 Q13; related: NTC 2081/05/07 objective Q21)

5. Derive the wave equation in free space and explain intrinsic impedance and the Poynting vector. [10]

6. State Maxwell’s equations and explain their physical meanings with boundary conditions. [10]

7. Explain Gauss’s law, Maxwell’s first equation and applications to symmetric charge distributions. [10]

8. Explain the Biot–Savart law and Ampere’s law with applications to standard current distributions. [10] (Related: NTC 2081/05/07 objective Q20)

9. Explain wave propagation in a perfect dielectric and lossy medium, including skin effect. [10] (Related: NTC 2082/03/30 Q4)

10. Explain waveguides, cutoff frequency, dominant mode and guide wavelength. [10]