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GATE Physics Electromagnetic Theory Syllabus
Every chapter and topic of Electromagnetic Theory examined in GATE Physics — 14 chapters, 8 topics, plus 51 flashcards written against it.
Electromagnetic Theory syllabus — full chapter and topic list
Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Electromagnetic Theory in GATE Physics, not a summary of it.
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Solutions of Electrostatic and Magnetostatic Problems
3 topics- Boundary Value Problems
- Method of Images
- Separation of Variables
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Dielectrics and Conductors
overviewExamined as a single unit within Electromagnetic Theory — no further topic split in the official outline.
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Magnetic Materials
overviewExamined as a single unit within Electromagnetic Theory — no further topic split in the official outline.
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Multipole Expansion
overviewExamined as a single unit within Electromagnetic Theory — no further topic split in the official outline.
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Maxwell's Equations
overviewExamined as a single unit within Electromagnetic Theory — no further topic split in the official outline.
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Scalar and Vector Potentials
overviewExamined as a single unit within Electromagnetic Theory — no further topic split in the official outline.
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Coulomb and Lorentz Gauges
overviewExamined as a single unit within Electromagnetic Theory — no further topic split in the official outline.
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Electromagnetic Waves
3 topics- In Free Space
- In Non-conducting Media
- In Conducting Media
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Reflection and Transmission
2 topics- At Normal Incidences
- At Oblique Incidences
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Polarization of Electromagnetic Waves
overviewExamined as a single unit within Electromagnetic Theory — no further topic split in the official outline.
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Poynting Vector
overviewExamined as a single unit within Electromagnetic Theory — no further topic split in the official outline.
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Poynting Theorem
overviewExamined as a single unit within Electromagnetic Theory — no further topic split in the official outline.
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Energy and Momentum of Electromagnetic Waves
overviewExamined as a single unit within Electromagnetic Theory — no further topic split in the official outline.
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Radiation from a Moving Charge
overviewExamined as a single unit within Electromagnetic Theory — no further topic split in the official outline.
Electromagnetic Theory flashcards for GATE Physics
23 of 51 cards from the Electromagnetic Theory deck — real questions with worked answers.
What general type of problem requires solving Laplace's or Poisson's equation subject to specified conditions on bounding surfaces?
A boundary value problem. You solve $\nabla^{2}V = -\frac{\rho}{\varepsilon_{0}}$ (Poisson) or $\nabla^{2}V = 0$ (Laplace) given $V$ or $\frac{\partial V}{\partial n}$ specified on the boundaries.
State the uniqueness theorem for electrostatic boundary value problems.
If the charge density in a region and the potential on all boundaries (or the boundary normal derivative) are specified, the solution of Poisson's/Laplace's equation in that region is unique.
What is the difference between Dirichlet and Neumann boundary conditions?
Dirichlet specifies the value of the potential $V$ on the boundary. Neumann specifies the normal derivative $\frac{\partial V}{\partial n}$ (i.e. the normal field/surface charge) on the boundary.
Write Laplace's equation in Cartesian coordinates.
$$\frac{\partial^{2}V}{\partial x^{2}} + \frac{\partial^{2}V}{\partial y^{2}} + \frac{\partial^{2}V}{\partial z^{2}} = 0$$
State the mean value property of solutions to Laplace's equation.
The potential $V$ at any point equals the average of $V$ over any spherical surface centered on that point. Consequently $V$ has no local maxima or minima inside a charge-free region.
In the method of images, what fundamental requirement must the image configuration satisfy?
The image charges must be placed only in the region outside where you want the field, and must reproduce the same boundary conditions (same $V$ on conductors) so that, by uniqueness, the field in the region of interest is identical to the real one.
For a point charge $q$ a distance $d$ above an infinite grounded conducting plane, what is the image charge and its location?
An image charge $-q$ located a distance $d$ behind the plane (at the mirror-image position). The plane is replaced by this $-q$.
Find the force on a point charge $q$ held a distance $d$ from an infinite grounded conducting plane.
$$F = -\frac{1}{4\pi\varepsilon_{0}}\frac{q^{2}}{(2d)^{2}} = -\frac{q^{2}}{16\pi\varepsilon_{0}d^{2}}$$ directed toward the plane (attractive).
What is the total induced surface charge on an infinite grounded plane due to a point charge $q$ at distance $d$?
The total induced charge equals $-q$ (equal and opposite to the image charge).
For the charge $q$ at distance $d$ above a grounded plane, write the induced surface charge density at distance $r$ from the foot of the perpendicular.
$$\sigma(r) = -\frac{q\,d}{2\pi\left(r^{2}+d^{2}\right)^{3/2}}$$
For a point charge $q$ outside a grounded conducting sphere of radius $R$ at distance $a$ from the center, what is the magnitude and position of the image charge?
Image charge $q' = -\frac{R}{a}q$, located at distance $b = \frac{R^{2}}{a}$ from the center, on the line joining the center to $q$.
What is the energy stored (work done) in bringing a charge $q$ from infinity to distance $d$ above a grounded plane?
$$W = -\frac{1}{4\pi\varepsilon_{0}}\frac{q^{2}}{4d} = -\frac{q^{2}}{16\pi\varepsilon_{0}d}$$ (half the value of two real charges, because the image is not a real charge).
In the separation of variables method, how is the potential assumed to factor in Cartesian coordinates?
As a product of single-variable functions: $V(x,y,z) = X(x)\,Y(y)\,Z(z)$, converting the PDE into ordinary differential equations linked by separation constants summing to zero.
After separating Laplace's equation in Cartesian coordinates, what constraint links the three separation constants?
$$k_{x}^{2} + k_{y}^{2} + k_{z}^{2} = 0$$ so they cannot all have the same sign; at least one direction gives oscillatory and another gives exponential/hyperbolic solutions.
Write the general separated solution of Laplace's equation in spherical coordinates with azimuthal symmetry.
$$V(r,\theta) = \sum_{l=0}^{\infty}\left(A_{l} r^{l} + \frac{B_{l}}{r^{l+1}}\right)P_{l}(\cos\theta)$$ where $P_{l}$ are Legendre polynomials.
In separation of variables, why is the completeness of the chosen functions (e.g. sines or Legendre polynomials) essential?
It allows any boundary potential to be expanded as a series in those functions, so the coefficients can be matched to satisfy the boundary conditions exactly (Fourier/Legendre coefficient determination).
Write Maxwell's four equations in free space (no charges or currents) in differential form.
$$\nabla\cdot\vec{E}=0,\quad \nabla\cdot\vec{B}=0,\quad \nabla\times\vec{E}=-\frac{\partial\vec{B}}{\partial t},\quad \nabla\times\vec{B}=\mu_{0}\varepsilon_{0}\frac{\partial\vec{E}}{\partial t}$$
What is the speed of an electromagnetic wave in free space in terms of $\mu_{0}$ and $\varepsilon_{0}$?
$$c = \frac{1}{\sqrt{\mu_{0}\varepsilon_{0}}} \approx 3\times10^{8}\ \text{m/s}$$
Write the electromagnetic wave equation for $\vec{E}$ in free space.
$$\nabla^{2}\vec{E} = \mu_{0}\varepsilon_{0}\frac{\partial^{2}\vec{E}}{\partial t^{2}}$$
For a plane EM wave in free space, what is the relationship between the magnitudes of $\vec{E}$ and $\vec{B}$?
$$E = cB \quad\Rightarrow\quad B = \frac{E}{c}$$
State the relative orientation of $\vec{E}$, $\vec{B}$, and the propagation direction $\hat{k}$ for a plane EM wave in free space.
They are mutually perpendicular and form a right-handed set: $\hat{k} = \hat{E}\times\hat{B}$. The wave is transverse.
Define the Poynting vector and give its expression.
It is the energy flux (power per unit area) carried by the EM field: $$\vec{S} = \frac{1}{\mu_{0}}\vec{E}\times\vec{B} = \varepsilon_{0}c^{2}\,\vec{E}\times\vec{B}$$
What is the time-averaged intensity of a plane EM wave in free space with amplitude $E_{0}$?
$$\langle S\rangle = \frac{1}{2}\varepsilon_{0}c E_{0}^{2} = \frac{E_{0}^{2}}{2\mu_{0}c}$$
Planning Electromagnetic Theory for GATE Physics
Electromagnetic Theory is about 7% of the GATE Physics syllabus by topic count — 8 of 123 topics, spread over 14 chapters. At roughly 45 minutes per topic plus 12 minutes per sub-topic, a first pass runs to about 6 hours.
The heaviest chapters are Solutions of Electrostatic and Magnetostatic Problems (3 topics), Electromagnetic Waves (3 topics), Reflection and Transmission (2 topics) . Front-load those while your energy is high; the short chapters are better revision filler later.
Work top-down: read the chapter, then tick topics off individually rather than marking the whole chapter done. Sub-topics are where silent gaps hide.
Electromagnetic Theory (GATE Physics) FAQ
What is in the GATE Physics Electromagnetic Theory syllabus?
Electromagnetic Theory is split into 14 chapters — Solutions of Electrostatic and Magnetostatic Problems, Dielectrics and Conductors, Magnetic Materials, Multipole Expansion, Maxwell's Equations and Scalar and Vector Potentials, and 8 more, containing 8 topics and 0 sub-topics in total.
How is Electromagnetic Theory structured in the GATE Physics syllabus?
14 chapters. Electromagnetic Theory accounts for about 7% of the topics in the whole GATE Physics syllabus (8 of 123).
How long should I spend on Electromagnetic Theory for GATE Physics?
Budget around 6 hours for a first pass through Electromagnetic Theory — about 45 minutes per topic plus 12 minutes per sub-topic across its 8 topics. Add revision cycles on top.
Are there flashcards for GATE Physics Electromagnetic Theory?
Yes — a 51-card Electromagnetic Theory deck. Sample cards are printed on this page, and the full deck is free in the Examius app with spaced repetition scheduling.