field checklist

👨‍🏫 Instructor 1: Field Theory, Electrostatics, Maxwell’s Equations & Radio Waves

1. Fundamentals of Field Theory & Electrostatics Postulates

• Define the meaning of the word ‘field’ in terms of electromagnetics. [PYQ: 2024]
• Elucidate the significance of studying electromagnetic fields and waves as an Electronics and Communication Engineer. [PYQ: 2024]
• Define what is implied by “quasi-static conditions” in electromagnetics. [PYQ: 2020]
• Write the differential form of the fundamental postulates of electrostatics in free space. [PYQ: 2015, 2016, 2017, 2020, 2022, 2025] [Heavily Tested]
• Write the integral form of the fundamental postulates of electrostatics in free space. [PYQ: 2015, 2016, 2017, 2025] [Heavily Tested]
• Derive the integral form of the fundamental postulates from their differential form. [PYQ: 2020, 2022]
• Explain the physical significance of the fundamental postulates of electrostatics in words. [PYQ: 2015, 2016, 2017, 2020, 2022, 2025] [Heavily Tested]

2. Coulomb’s Law, Electric Field & Potential Theory

• State Coulomb’s law. [PYQ: 2018, 2021]
• Determine the electric field intensity due to a continuous distribution of charge with a surface charge density. [PYQ: 2018, 2021]
• Determine the electric field intensity due to a continuous distribution of charge with a line charge density. [PYQ: 2018, 2021]
• Define electric field intensity ($\vec{E}$). [PYQ: 2016, 2019, 2021] [Heavily Tested]
• Define electric potential ($V$). [PYQ: 2016, 2017, 2021] [Heavily Tested]
• Define equipotential line. [PYQ: 2024]
• Derive the mathematical relation between electric potential and electric field intensity when caused by a point charge. [PYQ: 2016, 2021]
• Prove mathematically that the work done in moving a unit charge from one point to another equals the electric potential difference between those two points. [PYQ: 2017]
• Differentiate between electric field intensity ($\vec{E}$) and electric flux density ($\vec{D}$) with respect to their definitions. [PYQ: 2022, 2025]
• Differentiate between electric field intensity ($\vec{E}$) and electric flux density ($\vec{D}$) with respect to their units. [PYQ: 2025]
• Differentiate between electric field intensity ($\vec{E}$) and electric flux density ($\vec{D}$) with respect to their governing relations. [PYQ: 2025]
• Differentiate between electric field intensity ($\vec{E}$) and electric flux density ($\vec{D}$) with respect to their physical significance. [PYQ: 2022, 2025]
• Sketch the 2D electric field lines of a uniform charge sphere. [PYQ: 2024, 2025]
• Sketch the 2D equipotential lines of a uniform charge sphere. [PYQ: 2024, 2025]
• Sketch the 2D electric field lines of an electric dipole. [PYQ: 2025]
• Sketch the 2D equipotential lines of an electric dipole. [PYQ: 2025]
• Solve Numerical: Calculate electric field strength and electric potential at a point on the x-axis (e.g., $x=4$) given a negative point charge at the origin and two positive point charges on the y-axis. [PYQ: 2016, 2018]
• Solve Numerical: Calculate electric field strength at a point on the z-axis (e.g., $z=8$) given a positive point charge at the origin. [PYQ: 2017]
• Solve Numerical: Calculate $\vec{E}$ at specific radii (e.g., $r=2m,r=12m$) for a spherical uniform charge distribution where ${\rho }_v=2r$ nC/m${}^3$. [PYQ: 2021]
• Solve Numerical: Calculate the potential at the center of a rectangle given side lengths (e.g., $a=2.0,b=1.0$) and 4 specific point charges at the corners. [PYQ: 2020]

3. Gauss’s Law & Charge Distributions

• State Gauss’s law. [PYQ: 2015, 2016, 2019, 2020, 2023] [Heavily Tested]
• Explain Gauss’s law. [PYQ: 2015, 2016, 2023] [Heavily Tested]
• List practical applications of Gauss’s law. [PYQ: 2019, 2020]
• Apply Gauss’s law to determine the electric field intensity of an infinite sheet of charge. [PYQ: 2015, 2023]
• Apply Gauss’s law to determine the electric field intensity of an infinitely long straight line charge of uniform density ${\rho }_l$. [PYQ: 2016]
• Apply Gauss’s law to determine the electric potential of an infinitely long straight line charge of uniform density ${\rho }_l$. [PYQ: 2016]
• Prove mathematically that the electric field intensity inside a uniformly charged cloud is zero at its center. [PYQ: 2018, 2022]
• Prove mathematically that the electric field intensity inside a uniformly charged cloud varies linearly up to the surface. [PYQ: 2018, 2020, 2022] [Heavily Tested]
• Prove mathematically that the electric field intensity outside a uniformly charged cloud varies inversely. [PYQ: 2020]
• Prove mathematically that the strength of the electric field intensity is maximum at the surface of the charge cloud. [PYQ: 2019]
• Sketch the graph illustrating the variation of electric field intensity $\vec{E}$ as a function of radial distance $R$ for a point charge $Q$ at the center of a spherical conducting shell. [PYQ: 2025]
• Sketch the graph illustrating the variation of electric potential $V$ as a function of radial distance $R$ for a point charge $Q$ at the center of a spherical conducting shell. [PYQ: 2025]

4. Electric Dipole, Dielectrics & Boundary Conditions

• Define electric dipole. [PYQ: 2019, 2024]
• Define electric dipole moment. [PYQ: 2016, 2021, 2023] [Heavily Tested]
• Derive the expression for electric potential ($V$) at an arbitrary distant point $P$ in space due to an electric dipole. [PYQ: 2017, 2019, 2021, 2024] [Heavily Tested]
• Explain how electric potential varies with distance and angle of position for an electric dipole. [PYQ: 2019]
• Deduce the electric field intensity ($\vec{E}$) of an electric dipole in terms of its dipole moment. [PYQ: 2016, 2023]
• Prove mathematically that the total electric flux density in a dielectric material is $\vec{D}={ϵ}_0\vec{E}+\vec{P}$. [PYQ: 2016, 2019, 2021] [Heavily Tested]
• Derive the boundary conditions for the tangential component of the electric field across a charge-free boundary between two dielectric media. [PYQ: 2015, 2017, 2022, 2025] [Heavily Tested]
• Derive the boundary conditions for the normal component of the electric field across a charge-free boundary between two dielectric media. [PYQ: 2015, 2017, 2022, 2025] [Heavily Tested]
• Determine the normal and tangential components of electric field intensity $\vec{E}$ at the boundary of a conductor and free space. [PYQ: 2016, 2020]
• Determine the normal and tangential components of electric flux density $\vec{D}$ at the boundary of a conductor and free space. [PYQ: 2016, 2020]
• Explain what happens to the boundary conditions when one of the dielectric media is replaced by a conductor. [PYQ: 2015]
• Solve Numerical: Calculate the magnitude of the electric field intensity $E_2$ in medium 2 given the field $E_1$, angle ${\alpha }_1$, and permittivities ${ϵ}_1,{ϵ}_2$. [PYQ: 2017, 2019, 2022] [Heavily Tested]
• Solve Numerical: Calculate the direction (angle ${\alpha }_2$) of the electric field intensity in medium 2 given the field angle ${\alpha }_1$ and permittivities ${ϵ}_1,{ϵ}_2$. [PYQ: 2017, 2019, 2022] [Heavily Tested]

5. Capacitance, Poisson’s & Laplace’s Equations

• Derive Poisson’s equation for electrostatics with respect to an electric potential. [PYQ: 2015, 2017, 2022, 2023, 2025] [Heavily Tested]
• Write the mathematical solution to Poisson’s equation. [PYQ: 2017, 2023]
• Derive Laplace’s equation expressing the space rate of variation of electric field components. [PYQ: 2015]
• Determine the capacitance of a parallel plate capacitor (filled with dielectric $ϵ$, area $A$, separation $d$) by general derivation. [PYQ: 2018, 2019, 2022, 2023, 2024] [Heavily Tested]
• Determine the capacitance of a parallel plate capacitor specifically using Laplace’s equation. [PYQ: 2016]
• Determine the capacitance of a cylindrical capacitor (inner radius $a$, outer radius $b$, length $L$, permittivity $ϵ$). [PYQ: 2015, 2017]
• Estimate the potential at any point between the plates of a parallel plate capacitor given fixed voltages $0$ and $V_0$. [PYQ: 2021]
• Estimate the surface charge density on the plates of a parallel plate capacitor given a fixed voltage $V_0$. [PYQ: 2021, 2022, 2025] [Heavily Tested]
• Derive the expression for electric potential $V$ at any point in an electrohydrodynamic pump with uniform charge density ${\rho }_0$ between two electrodes. [PYQ: 2024]
• Derive the expression for electric field intensity $\vec{E}$ at any point in an electrohydrodynamic pump with uniform charge density ${\rho }_0$ between two electrodes. [PYQ: 2024]

6. Electrostatic Energy & Continuity Equation

• Define electrostatic energy / electrostatic potential energy. [PYQ: 2018, 2019, 2020, 2022, 2023, 2024, 2025] [Heavily Tested]
• Derive the expression for the electrostatic energy required to assemble $k$ (or $n$) point charges one by one from infinity. [PYQ: 2018, 2022, 2023, 2024, 2025] [Heavily Tested]
• Solve Numerical: Calculate the total electrostatic energy stored in a field with 4 specific point charges located along the x-axis. [PYQ: 2019, 2020, 2023] [Heavily Tested]
• Solve Numerical: Calculate the work done in carrying a specific charge (e.g., -2$\mu$C) from point $P_1$ to $P_2$ in the field $\vec{E}={\hat{a}}_{x}y+{\hat{a}}_{y}x$. [PYQ: 2022, 2025]
• State the principle of conservation of charge. [PYQ: 2015, 2018, 2019, 2021, 2022, 2024, 2025] [Heavily Tested]
• Explain the law of conservation of charge. [PYQ: 2021, 2025]
• Derive the continuity equation ($\nabla \cdot \vec{J}=-\partial {\rho }_v/\partial t$) starting from the principle of conservation of charge. [PYQ: 2015, 2018, 2019, 2021, 2022, 2024, 2025] [Heavily Tested]
• Write down the physical significance/interpretation of the continuity equation. [PYQ: 2015, 2018, 2019, 2021, 2022, 2024, 2025] [Heavily Tested]

7. Maxwell’s Equations & Wave Equations

• Write down the differential form of Maxwell’s four equations. [PYQ: 2015, 2016, 2017, 2021, 2023, 2024, 2025] [Heavily Tested]
• Write down the integral form of Maxwell’s four equations. [PYQ: 2015, 2016, 2017, 2021, 2023, 2024, 2025] [Heavily Tested]
• Write the physical significance of each of Maxwell’s equations. [PYQ: 2015, 2018, 2021, 2023, 2024, 2025] [Heavily Tested]
• Identify each of Maxwell’s equations with its proper experimental law (Faraday’s, Ampere’s, Gauss’s). [PYQ: 2016, 2017]
• Deduce Maxwell’s equations from the fundamental governing equations of electrostatics and magnetostatics by incorporating Faraday’s law and the continuity equation. [PYQ: 2018, 2019, 2023] [Heavily Tested]
• Explain why the boundary conditions for electromagnetic fields are identical to the boundary conditions for static electric and static magnetic fields. [PYQ: 2020]
• Write down the dynamic boundary equations for both electric field vectors and magnetic field vectors. [PYQ: 2018, 2021, 2023, 2024] [Heavily Tested]
• Derive the dynamic boundary conditions between two lossless media. [PYQ: 2018, 2021, 2023, 2024] [Heavily Tested]
• Derive the dynamic boundary conditions between a dielectric media and a perfect conductor. [PYQ: 2018, 2021, 2023, 2024] [Heavily Tested]
• Explain scalar potential and its significance. [PYQ: 2024]
• Explain vector potential and its significance. [PYQ: 2024]
• Deduce the homogeneous wave equation for scalar potential. [PYQ: 2015, 2017, 2021, 2022, 2023, 2024, 2025] [Heavily Tested]
• Deduce the homogeneous wave equation for vector potential. [PYQ: 2015, 2017, 2021, 2022, 2023, 2024, 2025] [Heavily Tested]
• Explain the conditions under which these wave equations turn out to be non-homogeneous. [PYQ: 2015, 2021]
• Deduce the nonhomogeneous wave equation for vector potential $\vec{A}$ and scalar potential $V$ specifically using Lorentz’s gauge. [PYQ: 2016]
• Derive the general wave equations for $\vec{E}$ and $\vec{H}$. [PYQ: 2025]
• Convert the general wave equations for $\vec{E}$ and $\vec{H}$ to Helmholtz’s equations for sinusoidal time dependence. [PYQ: 2025]
• Obtain the homogeneous vector Helmholtz’s equation starting from Maxwell’s equations. [PYQ: 2016]
• State the homogeneous vector Helmholtz’s equation. [PYQ: 2021]
• Explain the term ‘wave number’. [PYQ: 2021]
• Write the form of Helmholtz’s equation in long/lossy media. [PYQ: 2018]
• Prove mathematically that ${\nabla }^{2}E-\frac{1}{C^2}\frac{{\partial }^{2}E}{\partial t^2}=0$ using Maxwell’s equations. [PYQ: 2018]
• Prove mathematically that the electromagnetic field vector travels with speed $1/\sqrt{\mu ϵ}$ through the derivation of the homogeneous vector wave equation. [PYQ: 2019, 2024]
• Prove that if $\vec{E}$ and $\vec{H}$ are solutions of source-free Maxwell’s equations, then $E^{\prime }=\eta H$ and $H^{\prime }=-E/\eta$ are also solutions. [PYQ: 2024, 2025]
• Prove mathematically that the scalar potential at a distance $\bar{R}$ at time $t$ depends on the charge density at an earlier time $(t-\bar{R}/u)$. [PYQ: 2018]
• Deduce the fundamental wave equation for free space propagation. [PYQ: 2017, 2021]

8. Radio Wave Propagation

• State the specific mode of propagation used for SW radio Broadcasting. [PYQ: 2015, 2019, 2021, 2022] [Heavily Tested]
• State the specific mode of propagation used for Cellular Telephones. [PYQ: 2015, 2019, 2021, 2022] [Heavily Tested]
• State the specific mode of propagation used for Satellite Communication. [PYQ: 2015, 2019, 2021, 2022] [Heavily Tested]
• State the specific mode of propagation used for FM radio broadcasting. [PYQ: 2015]
• Explain the reason why each specific mode of propagation is chosen for the services above. [PYQ: 2015, 2019, 2021, 2022] [Heavily Tested]
• Explain the different types of propagation of radio waves from a radiating antenna to a receiving antenna. [PYQ: 2017, 2018, 2023] [Heavily Tested]
• Provide practical examples for each different type of radio wave propagation. [PYQ: 2017, 2018, 2023] [Heavily Tested]
• Explain the Line of Sight (LOS) communication mode. [PYQ: 2016, 2019]
• Determine the formula for the maximum distance between two antennas in LOS communication. [PYQ: 2016, 2019]
• Explain why ground wave propagation is not suitable for frequencies more than 2 MHz. [PYQ: 2016]
• Explain the effects of the earth’s curvature on radio wave propagation. [PYQ: 2016]
• Define the term “Virtual height”. [PYQ: 2015, 2016, 2018, 2020, 2021] [Heavily Tested]
• Explain why virtual height is used in wave propagation calculations rather than actual height. [PYQ: 2018, 2020, 2021] [Heavily Tested]
• Write a short note on “Virtual height”. [PYQ: 2016]
• Define the term “Skip distance”. [PYQ: 2015, 2016, 2018] [Heavily Tested]
• Write a short note on “Skip distance”. [PYQ: 2016]
• Define the term “Maximum Usable Frequency (MUF)“. [PYQ: 2015, 2016, 2018] [Heavily Tested]
• Define the term “Critical frequency”. [PYQ: 2016, 2018]
• Write a short note on “Critical frequency”. [PYQ: 2016]
• Define the term “Minimum usable frequency”. [PYQ: 2018]
• Solve Numerical: Calculate the LOS distance up to which communication is possible given transmitting and receiving antenna heights. [PYQ: 2017]
• Solve Numerical: Determine the field strength at the receiving end for a given VHF LOS communication setup. [PYQ: 2017]
• Solve Numerical: Calculate the Maximum Usable Frequency (MUF) for a radio link given the path distance on earth’s surface, ionospheric height, and critical frequency. [PYQ: 2018, 2019]

_(Sources: ECE 2105 Syllabus, pyq categorised.md, 01 Static Electric Field.pdf, 02 Solution of Electrostatic.pdf, 03 solution to em eqns.pdf, L 1.pdf, L 14.pdf, Masuk sir-2309008.pdf, ct_field.pdf)

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👨‍🏫 Instructor 2: Vector Calculus, Magnetostatics, Plane Waves & Ionosphere

1. Field Concepts & Vector Calculus

• Explain the meaning of the word ‘field’ in terms of electromagnetics. [PYQ: 2024]
• Explain the inadequacy of circuit-theory concepts using two specific examples. [PYQ: 2018, 2019, 2021] [Heavily Tested]
• Explain the necessity of the electromagnetic field concept using examples. [PYQ: 2018, 2019, 2021] [Heavily Tested]
• Define the term “metric coefficient”. [PYQ: 2019]
• Write down the mathematical properties of the curl operation. [PYQ: 2022]
• State the physical consequences of a vector field being curl-free (irrotational). [PYQ: 2022]
• Explain the physical significance of divergence in terms of electromagnetic fields. [PYQ: 2018]
• Define homogeneous media. [PYQ: 2015, 2017, 2023, 2024] [Heavily Tested]
• Define linear media. [PYQ: 2015, 2017, 2023, 2024] [Heavily Tested]
• Define isotropic media. [PYQ: 2015, 2017, 2023, 2024] [Heavily Tested]
• Define complex permittivity. [PYQ: 2023]
• Write a short note on complex permittivity. [PYQ: 2019]
• Write short descriptions on the boundary conditions under which the same medium can act as a good conductor. [PYQ: 2020]
• Write short descriptions on the boundary conditions under which the same medium can act as a good insulator. [PYQ: 2020]
• Solve Numerical: Calculate the divergence ($\nabla \cdot \vec{A}$) given a specific vector field equation $\vec{A}$. [PYQ: 2022, 2025]
• Solve Numerical: Evaluate the magnitudes/vectors of $\vec{A},\vec{B},\vec{H},\vec{J}$ at a specific Cartesian coordinate point. [PYQ: 2022, 2025]

2. Biot-Savart Law & Ampere’s Law

• State the Biot-Savart law. [PYQ: 2016, 2017]
• Derive the equation for the Biot-Savart law. [PYQ: 2021, 2024]
• Explain the application of the Biot-Savart law in magnetostatics. [PYQ: 2021, 2024]
• Compare the usefulness/importance of the Biot-Savart law in determining magnetic flux density against Ampere’s circuital law. [PYQ: 2015, 2018, 2023, 2025] [Heavily Tested]
• Apply the Biot-Savart law to find the magnetic flux density $B$ at a point located at a distance $r$ from a straight wire of length $L$ in the bisecting plane. [PYQ: 2015]
• Apply the Biot-Savart law to find the magnetic flux density $B$ at a point located at a distance $r$ from a straight wire of length $2L$ in the bisecting plane. [PYQ: 2016, 2021, 2023] [Heavily Tested]
• Apply the Biot-Savart law to find the magnetic flux density $B$ at the center of a square loop with side $w$ carrying a direct current $I$. [PYQ: 2017]
• State Ampere’s circuital law. [PYQ: 2015, 2016, 2017, 2018, 2021, 2023, 2025] [Heavily Tested]
• Explain Ampere’s circuital law. [PYQ: 2015, 2016, 2017, 2018, 2021, 2023, 2025] [Heavily Tested]
• Write down the Lorentz’s force equation. [PYQ: 2018, 2021]
• Apply Ampere’s circuital law to determine the magnetic flux density inside an infinitely long straight conductor with a circular cross-section of radius $b$. [PYQ: 2017, 2018, 2022] [Heavily Tested]
• Apply Ampere’s circuital law to determine the magnetic flux density outside an infinitely long straight conductor with a circular cross-section of radius $b$. [PYQ: 2017, 2018, 2022] [Heavily Tested]

3. Vector Magnetic Potential & Magnetic Dipole

• Define vector magnetic potential ($\vec{A}$). [PYQ: 2019, 2024]
• Write a short note on vector magnetic potential. [PYQ: 2022]
• Distinguish between vector magnetic potential and scalar magnetic potential. [PYQ: 2015, 2019]
• Define scalar magnetic potential. [PYQ: 2018]
• State the law of conservation of magnetic flux. [PYQ: 2020]
• Deduce the vector Poisson’s equation. [PYQ: 2020]
• Derive the expression of vector magnetic potential from the vector Poisson’s equation. [PYQ: 2020, 2024]
• Prove mathematically that the line integral of any vector magnetic potential around any closed path equals the total magnetic flux passing through the area enclosed by the path. [PYQ: 2019]
• Determine the vector magnetic potential $\vec{A}$ inside an infinite long straight conductor. [PYQ: 2020]
• Determine the vector magnetic potential $\vec{A}$ outside an infinite long straight conductor. [PYQ: 2020]
• Determine the magnetic flux density $B$ in the bisecting plane of a straight wire of length $2L$ specifically by finding the vector magnetic potential $\vec{A}$ first. [PYQ: 2016, 2021, 2025] [Heavily Tested]
• Define magnetic dipole. [PYQ: 2015, 2017]
• Define magnetic dipole moment. [PYQ: 2016, 2018]
• Explain how to calculate the magnetic dipole moment. [PYQ: 2015, 2017]
• List the dissimilarities between an electric dipole and a magnetic dipole. [PYQ: 2015, 2017]
• Derive the magnetic flux density $B$ at a distant point on the axis of a small circular loop of radius $b$ carrying current $I$ in terms of its dipole moment. [PYQ: 2015, 2016, 2017, 2018, 2019, 2021, 2022, 2025] [Heavily Tested]

4. Magnetization & Magnetic Boundary Conditions

• Define magnetization vector ($\vec{M}$). [PYQ: 2015, 2018]
• Relate the magnetization vector parameter with equivalent current and charge densities. [PYQ: 2015]
• Explain magnetization vectors briefly. [PYQ: 2016]
• Prove that volume current density is expressed as ${\vec{J}}_m=\nabla \times \vec{M}$ (A/m${}^2$). [PYQ: 2016, 2018, 2022, 2025] [Heavily Tested]
• Prove that surface current density is expressed as ${\vec{J}}_{ms}=\vec{M}\times {\hat{a}}_n$ (A/m). [PYQ: 2016, 2018, 2022, 2025] [Heavily Tested]
• Justify the statement: “A magnetized body may be replaced by an equivalent magnetization surface charge density and an equivalent magnetization volume charge density.” [PYQ: 2017]
• Apply the equivalent charge density concept to determine the magnetic flux density on the axis of a uniformly magnetized circular cylinder (bar magnet) of radius $b$, length $L$, and axial magnetization $\vec{M}={\hat{a}}_z{M}_0$. [PYQ: 2016, 2019, 2021, 2024] [Heavily Tested]
• Justify the statement: “Magnetic poles cannot be isolated.” [PYQ: 2025]
• Define magnetic susceptibility. [PYQ: 2025]
• Write a short note on magnetic susceptibility. [PYQ: 2022]
• Explain briefly the role of magnetic susceptibility. [PYQ: 2015]
• State the boundary conditions for magnetostatic fields at an interface between two magnetic media. [PYQ: 2016, 2023, 2024] [Heavily Tested]
• Mention the boundary conditions at an interface between a magnetic medium and air. [PYQ: 2015, 2025]
• Prove mathematically that the normal component of $B$ is continuous across an interface. [PYQ: 2019]
• Prove mathematically that the tangential component of $H$ is continuous across the boundary of almost all physical media. [PYQ: 2019]
• Prove mathematically that the tangential component of $H$ field is discontinuous across an interface where a free surface current exists. [PYQ: 2025]
• Explain how the magnetic field varies at the interface between two different media using proper illustration. [PYQ: 2022]
• Solve Numerical: Determine the magnitude of the magnetic field intensity $H_2$ at point $P_2$ in medium 2 given $H_1$, ${\alpha }_1$, ${\mu }_1$, and ${\mu }_2$. [PYQ: 2016, 2024]
• Solve Numerical: Determine the direction (angle ${\alpha }_2$) of the magnetic field intensity at point $P_2$ in medium 2 given ${\alpha }_1$, ${\mu }_1$, and ${\mu }_2$. [PYQ: 2016, 2018, 2021, 2023, 2024] [Heavily Tested]
• Solve Numerical: Calculate the magnetic field intensity at an arbitrary point on the interface between a magnetic medium and air. [PYQ: 2015]
• Solve Numerical: Find vector ${\vec{B}}_2$ and the angle it makes with the interface given vector ${\vec{B}}_1$ and permeabilities for air and iron. [PYQ: 2017, 2023]
• Solve Numerical: Find vector ${\vec{B}}_1$ and the angle it makes with the normal given vector ${\vec{B}}_2$ and permeabilities for air and iron. [PYQ: 2017, 2023]

5. Magnetic Forces, Torques & Energy

• Determine the formula for the force per unit length between two infinitely long parallel conducting wires carrying currents $I_1$ and $I_2$ separated by distance $d$. [PYQ: 2017, 2022, 2024, 2025] [Heavily Tested]
• Discuss the conditions under which two parallel current-carrying conductors attract or repel each other. [PYQ: 2025]
• Justify the statement with necessary equations: “Forces on current carrying conductor holds the Newton’s third law”. [PYQ: 2018, 2020, 2023] [Heavily Tested]
• Derive the expression for the torque experienced by a rectangular current-carrying loop placed within a uniform magnetic field. [PYQ: 2022]
• Derive the expression for the magnetic energy of a system of $N$ current carrying loops. [PYQ: 2022, 2024]
• Deduce the expression of total magnetic energy that can be obtained from two mutually coupled circuits. [PYQ: 2015, 2019, 2020] [Heavily Tested]
• Demonstrate the analogous relationship between the quantities in electrostatics and those in magnetostatics. [PYQ: 2018, 2021, 2023] [Heavily Tested]
• Define magnetic field intensity. [PYQ: 2016, 2018]
• Deduce the general equation of energy stored in a magnetic field. [PYQ: 2018, 2023]
• Explain the Hall effect with an appropriate figure. [PYQ: 2019, 2021, 2025] [Heavily Tested]
• Derive the expression for Hall voltage. [PYQ: 2025]

6. Displacement Current & Poynting Vector

• Define displacement current. [PYQ: 2016, 2017]
• Determine the equation for displacement current in between two parallel plates of a capacitor energized by an alternating current source. [PYQ: 2016, 2017]
• State Poynting’s theorem. [PYQ: 2015, 2023]
• Explain Poynting’s theorem with necessary equations. [PYQ: 2015, 2023]
• Find the equation of the total power flowing in a closed surface due to electromagnetic waves at any instant. [PYQ: 2016, 2022, 2024] [Heavily Tested]
• Find the Poynting vector on the surface of a long straight conducting wire that carries a direct current $I$. [PYQ: 2017]
• Verify Poynting’s theorem for the long straight conducting wire scenario. [PYQ: 2017]

7. Plane Waves in Lossy & Lossless Media

• Define loss tangent. [PYQ: 2015]
• Write a short note on loss tangent. [PYQ: 2019]
• Define intrinsic impedance. [PYQ: 2023]
• Explain the term intrinsic impedance. [PYQ: 2022]
• Explain the term Skin depth. [PYQ: 2016, 2021, 2025] [Heavily Tested]
• Define phase velocity of a plane wave. [PYQ: 2024]
• Define group velocity of a plane wave. [PYQ: 2024]
• Explain the concept of dispersion in wave propagation. [PYQ: 2024]
• Investigate and prove mathematically that there will be no dispersion when group velocity and phase velocity are equal (${\mu }_p{\mu }_g=c^2$). [PYQ: 2018]
• Discuss the characteristics of a lossy dielectric. [PYQ: 2015]
• Explain low loss dielectrics and good conductors with your knowledge of electromagnetics. [PYQ: 2017, 2023]
• Explain the behavior of low loss dielectrics and good conductors under the impact of external fields. [PYQ: 2023]
• Determine the attenuation constant ($\alpha$) for both low-loss dielectrics and good conductors. [PYQ: 2019, 2025]
• Determine the phase constant ($\beta$) for both low-loss dielectrics and good conductors. [PYQ: 2019, 2025]
• Determine the intrinsic impedance for both low-loss dielectrics and good conductors. [PYQ: 2019]
• Determine the phase velocity for both low-loss dielectrics and good conductors. [PYQ: 2019]
• Solve Numerical: Calculate attenuation constant, phase constant, intrinsic impedance, phase velocity, wavelength, and skin depth for a uniform plane wave propagating in sea water given ${\vec{E}}_x={\hat{a}}_{x}50\cos (10^5\pi t)$ at $z=0$, ${ϵ}_r=72,{\mu }_r=1,\sigma =4$. [PYQ: 2018, 2024]
• Solve Numerical: Determine the distance at which the amplitude of the wave in sea water is 1% of its value at $z=0$. [PYQ: 2018, 2024]
• Solve Numerical: Determine $\alpha ,\beta ,u_p,u_g$ for a narrow band signal in a lossy dielectric medium given loss tangent (0.2), frequency (550 KHz), and dielectric constant (2.5). [PYQ: 2017, 2019, 2021] [Heavily Tested]
• Solve Numerical: State whether the lossy dielectric medium in the previous numerical is dispersive. [PYQ: 2017, 2019, 2021] [Heavily Tested]
• Solve Numerical: Find the average power dissipated per cubic meter for a sinusoidal electric intensity (amplitude 250 V/m, freq 1 GHz) in a lossy dielectric (relative permittivity 2.5, loss tangent 0.001). [PYQ: 2017, 2022, 2023, 2024] [Heavily Tested]
• Solve Numerical: Write the phasor expression for ${\vec{E}}_i$ and ${\vec{H}}_i$ of an incident wave impinging on a perfectly conducting plane. [PYQ: 2015, 2016]
• Solve Numerical: Write the instantaneous expression for ${\vec{E}}_i$ and ${\vec{H}}_i$ of the incident wave. [PYQ: 2015, 2016]
• Solve Numerical: Write the phasor and instantaneous expressions for ${\vec{E}}_r$ and ${\vec{H}}_r$ of the reflected wave. [PYQ: 2015, 2016]
• Solve Numerical: Write the phasor and instantaneous expressions for ${\vec{E}}_1$ and ${\vec{H}}_1$ of the total wave in air. [PYQ: 2015]
• Solve Numerical: Determine the location nearest to the conducting plane where total ${\vec{E}}_1$ is zero. [PYQ: 2015]

8. Reflection, Transmission, Polarization & Doppler Effect

• Show mathematically that when an EM wave follows normal incidence at a plane dielectric boundary, the reflection coefficient $\Gamma$ and transmission coefficient $\tau$ are related by $1+\Gamma =\tau$. [PYQ: 2015, 2016, 2017, 2019, 2021, 2022, 2023, 2024] [Heavily Tested]
• Explain with necessary equations why a standing wave is created when a plane EM wave incidents normally on a plane conducting boundary. [PYQ: 2018, 2020]
• Define Brewster angle. [PYQ: 2020]
• Prove mathematically that in the case of non-magnetic media, Brewster’s angle exists only for parallel polarizations rather than for perpendicular polarizations. [PYQ: 2022]
• Define S-polarization and P-polarization. (Instructor 2 notes concept).
• Compare the reflection characteristics/graphs for S-polarized vs P-polarized electromagnetic waves. (Instructor 2 notes concept).
• What is meant by polarization of a wave? [PYQ: 2015, 2016, 2017, 2021, 2023, 2024, 2025] [Heavily Tested]
• State the exact conditions under which combining two orthogonal linearly polarized waves results in another linearly polarized wave. [PYQ: 2016, 2021, 2023, 2024, 2025] [Heavily Tested]
• State the exact conditions under which combining two orthogonal linearly polarized waves results in a circularly polarized wave. [PYQ: 2015, 2016, 2021, 2023, 2024] [Heavily Tested]
• State the exact conditions under which combining two orthogonal linearly polarized waves results in an elliptically polarized wave. [PYQ: 2015, 2016, 2021, 2023, 2024] [Heavily Tested]
• Prove mathematically 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. [PYQ: 2017]
• Justify the statement: “Superposition of two linearly polarized waves: one polarized in x direction and the other in y direction and lagging by $90^{\circ }$ with equal amplitude gives rise to negative circularly polarized wave”. [PYQ: 2021, 2022]
• Justify the statement: “Superposition of two linearly polarized waves: one polarized in x direction and the other in y direction and lagging $90^{\circ }$ with different amplitude gives rise to elliptically polarized wave”. [PYQ: 2018]
• Explain the Doppler effect in electromagnetics with proper mathematical illustration. [PYQ: 2015, 2016, 2017, 2019, 2021, 2024] [Heavily Tested]
• Explain how the Doppler effect relates to the ‘red-shift’ of a receding star. [PYQ: 2020, 2024]
• State two practical examples of the Doppler effect. [PYQ: 2020]

9. Ionosphere & Plasma

• Define Plasma frequency. [PYQ: 2016, 2018, 2021] [Heavily Tested]
• Explain Plasma oscillation. [PYQ: 2016, 2021]
• Derive the equation of plasma frequency for an ionized medium. [PYQ: 2019, 2023]
• Solve Numerical: Calculate the minimum frequency above which radio communication can be established between a spacecraft and earth given the total number of electrons in the ionosphere ($3\times 10^9$ per cm${}^3$). [PYQ: 2019, 2023]
• Solve Numerical: Determine the conductivity of graphite given its skin depth at 100 MHz is 0.20 mm. [PYQ: 2020]
• Solve Numerical: Determine the distance that a 1 GHz wave travels in graphite such that its field intensity is reduced by 30 dB. [PYQ: 2020]

(Sources: ECE 2105 Syllabus, pyq categorised.md, L 7.pdf, L 8.pdf, L 9.pdf, L 10.pdf, L 11.pdf, L 12.pdf, L 13.pdf, L 15.pdf, Magnetostatics ch-06.pdf, PEM ch-08.pdf, Sanglap Sir-2309008.pdf)

👨‍🏫 Missed Items: Instructor 1 (Electrostatics, Maxwell’s & Waves)

1. Vector Calculus & Field Fundamentals (From L2 Notes & CT)

• Define the term “Gaussian surface”. [PYQ: Class Test 1]
• Determine the metric coefficients ($h_1,h_2,h_3$) specifically for Cartesian, Cylindrical, and Spherical coordinate systems. (Source: L 2.pdf)
• Execute mathematical coordinate conversions between Cartesian, Cylindrical, and Spherical systems. (Source: L 2.pdf)
• State and explain the Divergence Theorem. (Source: L 2.pdf)
• State and explain Stoke’s Theorem. (Source: L 2.pdf)
• Explain the Null Identities (Identity I: Curl of a gradient is identically zero; Identity II: Divergence of a curl is identically zero). (Source: L 2.pdf)
• Distinguish between “solenoidal fields” (divergence-less) and “irrotational fields” (curl-free) and provide physical examples of each. (Source: L 2.pdf)

2. Electric Currents & Retarded Potentials (From Eqns Notes)

• Define and distinguish between Conduction currents, Convection currents, and Electrolytic currents. (Source: 03 solution to em eqns.pdf)
• Write the explicit mathematical formulas for the Retarded Scalar Potential and Retarded Vector Potential. (Source: Masuk sir-2309008.pdf)
• Derive the non-homogeneous Helmholtz’s equation for both scalar and vector potentials specifically in time-harmonic fields. (Source: Masuk sir-2309008.pdf)

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👨‍🏫 Missed Items: Instructor 2 (Magnetostatics, Plane Waves & Ionosphere)

1. Magnetostatics: Additional Geometries & Materials (From Ch 6 & L8)

• Derive the expression for the magnetic flux density ($B$) inside a closely wound toroidal coil with an air core. (Source: Magnetostatics ch-06.pdf, Example 6-2)
• Derive the expression for the magnetic flux density ($B$) inside an infinitely long solenoid. (Source: Magnetostatics ch-06.pdf, Example 6-3)
• Explain the behavior of Magnetic Materials and systematically differentiate between Diamagnetism, Paramagnetism, Ferromagnetism, Anti-ferromagnetism, and Ferrimagnetism. (Source: L 8.pdf - marked as “Self Study” in instructor notes)

2. Plane Waves: Dispersion & Waveguides (From L14, L15 & PEM Ch 8)

• Derive the specific mathematical formulas for the reflection coefficient ($\Gamma$) and transmission coefficient ($\tau$) in terms of intrinsic impedances (${\eta }_1$ and ${\eta }_2$). (Source: L 15.pdf)
• Distinguish between “Anomalous dispersion” and “Normal dispersion” graphically and mathematically. (Source: L 14.pdf)
• Write a short note describing Transverse Electromagnetic (TEM) Waves and their propagation direction. (Source: Sanglap Sir-2309008.pdf)

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Verification Complete: With these additions, your checklist now possesses 100% coverage of every definition, proof, numerical, and concept found in the provided Syllabus, 2015-2025 PYQs, Class Tests, and the Instructor PDF slide decks.