## Marks 1

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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, thin...
GATE ECE 2017 Set 2
Faraday's law of electromagnetic induction is mathematically described by which one of the following equations?
GATE ECE 2016 Set 3
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
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
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
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
The divergence of the vector field $$\overrightarrow A\;=\;x{\widehat a}_x\;+\;y{\widehat a}_y\;+\;z{\widehat a}_z$$ is
GATE ECE 2013
Consider a closed surface S surrounding volume V. If $$\overrightarrow{\mathrm r}$$ is the position vector of a point i...
GATE ECE 2011
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
If C is a closed curve enclosing a surface S, then the magnetic field intensity $$\overrightarrow H$$, the current dens...
GATE ECE 2007
$$\int\int\left(\nabla\times\mathrm P\right)\;\cdot\mathrm{ds}$$ , where is a vector, is equal to
GATE ECE 2006
$$\nabla \times \nabla \times P$$, where P is a vector, is equal to
GATE ECE 2006
The unit of $$\nabla\times\mathrm H$$ is
GATE ECE 2003
An electric field on a plane is described by its potential V = $$20\left(r^{-1}\;+\;r^{-2}\right)$$ where r is the dist...
GATE ECE 1999
Identify which one of the following will NOT satisfy the wave equation.
GATE ECE 1999
The Maxwell's equation $$\nabla\times\overrightarrow H\;=\;\overrightarrow J\;+\;\frac{\partial\overrightarrow D}{\parti... GATE ECE 1998 A loop is rotating about the y-axis in a magnetic field$$\$\overrightarrow B\;=\;B_0\cos\left(\mathrm{ωt}\;+\;\mathrm\ph...
GATE ECE 1998
The time averaged Poynting vector, in W/m2, for a wave with $$\vec E = 24{e^{j\left( {\omega t + \beta z} \right)}}{\mke... GATE ECE 1998 A metal sphere with 1 m radius and a surface charge density of 10 Coulombs/m2 is enclosed in a cube of 10 m side. The ... GATE ECE 1996 The electric field strength at a distance point, P, due to a point charge, +q, located at the origin, is 100$$\mu $$V/... GATE ECE 1995 In the infinite plane, y = 6 m, there exists a uniform surface charge density of (1/6000$$\pi $$)$$\mu $$C/m2. The ass... GATE ECE 1995 ... GATE ECE 1994 ## Marks 2 More An electron (q1) is moving in free space with velocity 105 m/s towards a stationary electron (q2) far away. The closest ... GATE ECE 2017 Set 2 The parallel-plate capacitor shown in the figure has movable plates. The capacitor is charged so that the energy stored ... GATE ECE 2016 Set 2 A coaxial capacitor of inner radius 1 mm and outer radius 5 mm has a capacitance per unit length of 172 pF/m. If the rat... GATE ECE 2015 Set 3 If$$\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
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
Given the vector $$\mathrm A=\left(\cos\;\mathrm x\right)\left(\sin\;\mathrm y\right)\;{\widehat{\mathrm a}}_\mathrm x\... GATE ECE 2014 Set 3 An infinitely long uniform solid wire of radius a carries a uniform dc current of density$$\widehat{\mathrm j}$$The ma... GATE ECE 2012 An infinitely long uniform solid wire of radius a carries a uniform dc current of density$$\widehat{\mathrm j}$$. A hol... GATE ECE 2012 If$$\overrightarrow{\mathrm A}\;=\;\mathrm{xy}\;{\widehat{\mathrm a}}_\mathrm x\;+\;\mathrm x^2\;{\widehat{\mathrm a}}_...
GATE ECE 2010
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
If the electric field intensity is given by $$\mathrm E=\left(\mathrm x{\widehat{\mathrm u}}_\mathrm x\;+\mathrm y{\wide... GATE ECE 2003 A material has conductivity of 10-2 mho/m and a relative permittivity of 4. The frequency at which the conduction curren... GATE ECE 2001 Given,$$\overrightarrow V=x\cos^2y\;\;\widehat{\mathrm i}\;+\;\mathrm x^2\mathrm e^\mathrm z\;\widehat{\mathrm j}\;+\;\m...
GATE ECE 1993
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
Which of the following field equations indicate that the free magnetic charges do not exits?
GATE ECE 1990
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
Vector potential is a vector
GATE ECE 1988
On either side of a charge-free interface between two media,
GATE ECE 1988
An electrostatic field is said to be conservative when
GATE ECE 1987
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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