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GATE ECE
Maxwell Equations
Electromagnetics
Previous Years Questions
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Marks 1
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In an electrostatic field, the electric displacement density vector, $$\overrightarrow D $$, is given by $$\overrightarr...
GATE ECE 2022
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In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amper...
GATE ECE 2022
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Two conducting spheres S1 and S2 of radii a and b (b>a) respectively, are placed far apart and connected by a long, t...
GATE ECE 2017 Set 2
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Faraday's law of electromagnetic induction is mathematically described by which one of the following equations?
GATE ECE 2016 Set 3
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Consider the time-varying vector $$I = \,\hat x\,\,15\,\cos \,(\omega \,t) + \,\hat y\,5\,sin(\omega \,t)$$ in Cartesian...
GATE ECE 2016 Set 2
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A uniform and constant magnetic field $$B=\widehat zB$$ exists in the $$\widehat z$$ direction in vacuum. A particle of ...
GATE ECE 2016 Set 2
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Concentric spherical shells of radii 2 m, 4 m, and 8 m carry uniform surface charge densities of 20 nC/m2 , −4 nC/m2 and...
GATE ECE 2016 Set 1
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In a source free region in vacuum, if the electrostatic potential $$\varphi\;=\;2x^2\;+y^2+cz^2$$ , the value of constan...
GATE ECE 2015 Set 2
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The divergence of the vector field $$\overrightarrow A\;=\;x{\widehat a}_x\;+\;y{\widehat a}_y\;+\;z{\widehat a}_z$$ is
GATE ECE 2013
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Consider a closed surface S surrounding volume V. If $$\overrightarrow{\mathrm r}$$ is the position vector of a point i...
GATE ECE 2011
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Two infinitely long wires carrying current are as shown in the figure below. One wire is in the y-z plane and parallel t...
GATE ECE 2009
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If C is a closed curve enclosing a surface S, then the magnetic field intensity $$\overrightarrow H $$, the current dens...
GATE ECE 2007
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$$\nabla \times \nabla \times P$$, where P is a vector, is equal to
GATE ECE 2006
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$$\int\int\left(\nabla\times\mathrm P\right)\;\cdot\mathrm{ds}$$ , where is a vector, is equal to
GATE ECE 2006
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The unit of $$\nabla\times\mathrm H$$ is
GATE ECE 2003
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Identify which one of the following will NOT satisfy the wave equation.
GATE ECE 1999
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An electric field on a plane is described by its potential V = $$20\left(r^{-1}\;+\;r^{-2}\right)$$ where r is the dista...
GATE ECE 1999
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The time averaged Poynting vector, in W/m2, for a wave with $$\vec E = 24{e^{j\left( {\omega t + \beta z} \right)}}{\mke...
GATE ECE 1998
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A loop is rotating about the y-axis in a magnetic field $$$\overrightarrow B\;=\;B_0\cos\left(\mathrm{ωt}\;+\;\mathrm\ph...
GATE ECE 1998
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The Maxwell's equation $$\nabla\times\overrightarrow H\;=\;\overrightarrow J\;+\;\frac{\partial\overrightarrow D}{\parti...
GATE ECE 1998
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A metal sphere with 1 m radius and a surface charge density of 10 Coulombs/m2 is enclosed in a cube of 10 m side. The ...
GATE ECE 1996
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In the infinite plane, y = 6 m, there exists a uniform surface charge density of (1/6000$$\pi $$) $$\mu $$C/m2. The asso...
GATE ECE 1995
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The electric field strength at a distance point, P, due to a point charge, +q, located at the origin, is 100 $$\mu $$V/...
GATE ECE 1995
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...
GATE ECE 1994
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Marks 2
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An electron (q1) is moving in free space with velocity 105 m/s towards a stationary electron (q2) far away. The closest ...
GATE ECE 2017 Set 2
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The parallel-plate capacitor shown in the figure has movable plates. The capacitor is charged so that the energy stored ...
GATE ECE 2016 Set 2
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A coaxial capacitor of inner radius 1 mm and outer radius 5 mm has a capacitance per unit length of 172 pF/m. If the rat...
GATE ECE 2015 Set 3
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The electric field (assumed to be one-dimensional) between two points A and B is shown. Let $$\psi_A$$ and $$\psi_B$$ be...
GATE ECE 2014 Set 4
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Given the vector $$$\mathrm A=\left(\cos\;\mathrm x\right)\left(\sin\;\mathrm y\right)\;{\widehat{\mathrm a}}_\mathrm x\...
GATE ECE 2014 Set 3
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If $$\overrightarrow{\mathrm E}=-\left(2\mathrm y^2\;-3\mathrm{yz}^2\right)\widehat{\mathrm x}\;-\left(6\mathrm{xy}^2-3\...
GATE ECE 2014 Set 4
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An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$ The ma...
GATE ECE 2012
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An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$. A hol...
GATE ECE 2012
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If $$\overrightarrow{\mathrm A}\;=\;\mathrm{xy}\;{\widehat{\mathrm a}}_\mathrm x\;+\;\mathrm x^2\;{\widehat{\mathrm a}}_...
GATE ECE 2010
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The value of the integral of the function $$\mathrm g\left(\mathrm x,\mathrm y\right)=4\mathrm x^3\;+\;10\mathrm y^4$$ a...
GATE ECE 2008
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If the electric field intensity is given by $$\mathrm E=\left(\mathrm x{\widehat{\mathrm u}}_\mathrm x\;+\mathrm y{\wide...
GATE ECE 2003
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A material has conductivity of 10-2 mho/m and a relative permittivity of 4. The frequency at which the conduction curren...
GATE ECE 2001
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Given,$$\overrightarrow V=x\cos^2y\;\;\widehat{\mathrm i}\;+\;\mathrm x^2\mathrm e^\mathrm z\;\widehat{\mathrm j}\;+\;\m...
GATE ECE 1993
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Which of the following field equations indicate that the free magnetic charges do not exits?
GATE ECE 1990
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The incoming solar radiation at a place on the surface of the earth is 1.2 KW/m2.The amplitude of the electric field cor...
GATE ECE 1990
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The electric field strength at a far-off point P due to a point charge + q, located at the origin O is 100 millivolts/me...
GATE ECE 1989
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On either side of a charge-free interface between two media,
GATE ECE 1988
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Vector potential is a vector
GATE ECE 1988
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Two long parallel wires in free space are separated by a distance R and carry currents of equal magnitude but opposite i...
GATE ECE 1987
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An electrostatic field is said to be conservative when
GATE ECE 1987
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