GATE E&C Engineering Electromagnetics Syllabus

Electromagnetics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Electromagnetics in GATE E&C Engineering, not a summary of it.

1. 1

   Maxwell's Equations

   5 topics

   • Differential and Integral Forms
   • Interpretation
   • Boundary Conditions
   • Wave Equation
   • Poynting Vector
2. 2

   Plane Waves and Properties

   5 topics

   • Reflection and Refraction
   • Polarization
   • Phase and Group Velocity
   • Propagation Through Various Media
   • Skin Depth
3. 3

   Transmission Lines

   6 topics

   • Equations
   • Characteristic Impedance
   • Impedance Matching
   • Impedance Transformation
   • S-parameters
   • Smith Chart
4. 4

   Rectangular and Circular Waveguides

   1 topic

   • Light Propagation in Optical Fibers
5. 5

   Dipole and Monopole Antennas

   overview

   Examined as a single unit within Electromagnetics — no further topic split in the official outline.

6. 6

   Linear Antenna Arrays

   overview

   Examined as a single unit within Electromagnetics — no further topic split in the official outline.

Electromagnetics flashcards for GATE E&C Engineering

20 of 51 cards from the Electromagnetics deck — real questions with worked answers.

1. State Maxwell's equation for Gauss's law (electric) in both differential and integral form.

   Differential: $\nabla \cdot \vec{D} = \rho_v$. Integral: $\oint_S \vec{D} \cdot d\vec{S} = \int_V \rho_v \, dV = Q_{enc}$.

2. State Gauss's law for magnetism (Maxwell) in differential and integral form, and its physical meaning.

   Differential: $\nabla \cdot \vec{B} = 0$. Integral: $\oint_S \vec{B} \cdot d\vec{S} = 0$. Meaning: there are no magnetic monopoles; magnetic field lines are continuous (closed loops).

3. Write Faraday's law of induction (Maxwell) in differential and integral form.

   Differential: $\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$. Integral: $\oint_C \vec{E} \cdot d\vec{l} = -\frac{d}{dt}\int_S \vec{B} \cdot d\vec{S}$.

4. Write Ampère's law with Maxwell's correction in differential and integral form.

   Differential: $\nabla \times \vec{H} = \vec{J} + \frac{\partial \vec{D}}{\partial t}$. Integral: $\oint_C \vec{H} \cdot d\vec{l} = \int_S \left(\vec{J} + \frac{\partial \vec{D}}{\partial t}\right) \cdot d\vec{S}$.

5. What is the displacement current density and why did Maxwell introduce it?

   Displacement current density is $\vec{J}_d = \frac{\partial \vec{D}}{\partial t}$. Maxwell introduced it so that Ampère's law remains consistent in time-varying fields (e.g., a charging capacitor) and to satisfy the continuity equation, enabling EM wave propagation.

6. State the continuity equation (charge conservation) in differential form.

   $$\nabla \cdot \vec{J} = -\frac{\partial \rho_v}{\partial t}$$

7. Give the constitutive relations linking the field quantities in a linear, isotropic medium.

   $\vec{D} = \varepsilon \vec{E}$, $\vec{B} = \mu \vec{H}$, and $\vec{J} = \sigma \vec{E}$ (Ohm's law in point form), where $\varepsilon$, $\mu$, $\sigma$ are permittivity, permeability, and conductivity.

8. What is the physical interpretation of $\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$?

   A time-varying magnetic field induces a circulating (rotational) electric field. The negative sign expresses Lenz's law: the induced EMF opposes the change in magnetic flux.

9. State the boundary condition on the tangential electric field at the interface between two media.

   The tangential component of $\vec{E}$ is continuous: $E_{t1} = E_{t2}$, i.e. $\hat{n} \times (\vec{E}_1 - \vec{E}_2) = 0$.

10. State the boundary condition on the normal component of $\vec{D}$ at an interface.

    $D_{n1} - D_{n2} = \rho_s$, i.e. $\hat{n} \cdot (\vec{D}_1 - \vec{D}_2) = \rho_s$. The normal $\vec{D}$ is discontinuous by the surface charge density $\rho_s$.

11. State the boundary conditions on tangential $\vec{H}$ and normal $\vec{B}$ at an interface.

    Tangential $\vec{H}$: $\hat{n} \times (\vec{H}_1 - \vec{H}_2) = \vec{J}_s$ (continuous if no surface current). Normal $\vec{B}$: $B_{n1} = B_{n2}$ (always continuous).

12. At the surface of a perfect electric conductor (PEC), what are the field boundary conditions?

    Tangential $\vec{E} = 0$, normal $\vec{B} = 0$ inside/at surface; normal $\vec{D} = \rho_s$ and tangential $\vec{H} = \vec{J}_s$. Fields exist only normal-$E$ and tangential-$H$ at the surface.

13. Derive/state the wave equation for $\vec{E}$ in a source-free, lossless dielectric.

    $$\nabla^2 \vec{E} = \mu \varepsilon \frac{\partial^2 \vec{E}}{\partial t^2}$$ This is the homogeneous Helmholtz/wave equation with wave speed $u = \frac{1}{\sqrt{\mu \varepsilon}}$.

14. What is the velocity of an EM wave in free space and the underlying formula?

    $u = c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \approx 3 \times 10^{8}\ \text{m/s}$, where $\mu_0 = 4\pi \times 10^{-7}\ \text{H/m}$ and $\varepsilon_0 \approx 8.854 \times 10^{-12}\ \text{F/m}$.

15. For a uniform plane wave $\vec{E} = E_0 e^{j(\omega t - \beta z)}\hat{x}$, define the phase constant and wavelength.

    Phase constant $\beta = \omega \sqrt{\mu \varepsilon} = \frac{2\pi}{\lambda}$; wavelength $\lambda = \frac{2\pi}{\beta} = \frac{u}{f}$. Phase velocity $u_p = \frac{\omega}{\beta}$.

16. Define the intrinsic (characteristic) impedance of a medium and give its free-space value.

    $\eta = \sqrt{\frac{\mu}{\varepsilon}}$, the ratio $\frac{E}{H}$ of a plane wave. In free space $\eta_0 = \sqrt{\frac{\mu_0}{\varepsilon_0}} \approx 377\ \Omega = 120\pi\ \Omega$.

17. What is the Poynting vector and what does it represent?

    $\vec{P} = \vec{E} \times \vec{H}$ (units $\text{W/m}^2$). It represents the instantaneous power flux density (direction and magnitude of EM power flow per unit area).

18. Give the expression for time-average power density (average Poynting vector) for a sinusoidal field.

    $$\vec{P}_{avg} = \frac{1}{2}\,\text{Re}\left(\vec{E} \times \vec{H}^{*}\right)$$ For a plane wave: $P_{avg} = \frac{E_0^2}{2\eta}$.

19. State Poynting's theorem in words.

    The net EM power flowing out of a closed surface equals the rate of decrease of stored electric and magnetic energy inside, minus the ohmic power dissipated. It is the energy-conservation statement for EM fields.

20. Define the loss tangent and what it distinguishes.

    Loss tangent $\tan\delta = \frac{\sigma}{\omega \varepsilon} = \frac{J_c}{J_d}$ (ratio of conduction to displacement current). It classifies media: $\tan\delta \ll 1$ good dielectric; $\tan\delta \gg 1$ good conductor.

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