56 solved GATE EE questions on Electromagnetic Fields, drawn from 13 exam years and grouped by year. Every question shows the official answer and a step-by-step solution.
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Identify the charge or current distribution's symmetry before selecting a Gaussian surface or Amperian loop. These selected foundations connect electrostatics, magnetostatics, Maxwell's equations, and wave propagation through original exercises. State boundary conditions and medium properties explicitly.
Our study notes and original examples support the PYQs below; they are not official exam questions or a replacement for the current syllabus.
The electric field from a point charge Q in free space is E = Q/(4πε₀r²) directed radially. Potential is V = Q/(4πε₀r), defined relative to a zero reference. E = −∇V relates field to potential. Superposition applies for multiple charges.
Check yourself: Is your reference potential at infinity, and does the field point from high to low potential?
Gauss's law in integral form states ∮ D·dS = Q_enc. In differential form, ∇·D = ρ_v. Choose a Gaussian surface that exploits symmetry so D is constant on the surface and either parallel or perpendicular to dS. Without symmetry, use superposition or the differential form.
Check yourself: Is D constant in magnitude and aligned with the surface normal everywhere on your Gaussian surface?
The Biot–Savart law gives the magnetic field from a current element: dB = μ₀ I dl × r̂ / (4πr²). Ampère's law ∮ H·dl = I_enc simplifies calculations when current symmetry allows H to be factored out of the integral. The right-hand rule determines field direction.
Check yourself: Does your Ampèrian loop lie on a surface where H is constant and tangential?
Maxwell's four equations unify electrostatics, magnetostatics, and time-varying fields. At a boundary between two media, the tangential component of E and the normal component of B are continuous (in the absence of surface charge and current). Boundary conditions determine reflection and transmission of waves.
Check yourself: Have you matched both tangential and normal components at the interface?
In a lossless medium, a uniform plane wave has E and H perpendicular to each other and to the propagation direction. The intrinsic impedance is η = √(μ/ε), and the phase velocity is v_p = 1/√(με). In free space, η₀ = 120π ≈ 377 Ω and v_p = c.
Check yourself: Are E, H, and the propagation direction mutually orthogonal and right-handed?
Original teaching example · not a PYQ
Original mini-example: a solid sphere of radius R carries a uniform volume charge density ρ C/m³ in free space. Using Gauss's law, find the electric field magnitude at distance r from the centre for r < R and r > R.
E = ρr/(3ε₀) for r < R; E = ρR³/(3ε₀r²) for r > R; both directed radially outward.
The electric field in a region of free space is E = 5r r̂ V/m in spherical coordinates, where r is the radial distance in metres. Find the volume charge density using Gauss's law in differential form.
ρ_v = 15ε₀ C/m³, approximately 132.8 pC/m³.
In spherical coordinates with a purely radial field, ∇·E = (1/r²) d(r² × 5r)/dr = (1/r²) d(5r³)/dr = 15r²/r² = 15 V/m². From ∇·D = ρ_v and D = ε₀E: ρ_v = 15ε₀ ≈ 15 × 8.854 × 10⁻¹² C/m³.
Supplemental reading, not an official GATE reading list or an endorsement of these notes.
Free supplemental textbook by Markus Zahn covering electrostatics, magnetostatics, Maxwell's equations, and wave propagation with worked problems.
This page shows 56 recent questions from the released archive, newest first. For older questions and complete papers, browse all GATE EE papers. Questions can carry more than one subject tag; counts are not marks weightage.
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