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GATE2020EC: 2
For a vector field $\overrightarrow{A}$, which one of the following is $\text{FALSE}$? $\overrightarrow{A}$ is solenoidal if $\triangledown \cdot \overrightarrow{A}=0.$ $\triangledown \times \overrightarrow{A}$ ...
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Feb 13
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jothee
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gate2020ec
engineeringmathematics
vectors
overrightarrow
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2
GATE2020EC: 45
The magnetic field of a uniform plane wave in vacuum is given by $\overrightarrow{H}\left ( x,y,z,t \right )=(\hat{a_{x}}+2\hat{a_{y}}+b\hat{a_{z}})\cos\left ( \omega t+3xyz\right ).$ The value of $b$ is ___________.
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Feb 13
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gate2020ec
numericalanswers
overrightarrow
vectoralgebra
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3
GATE2019 EC: 36
Two identical copper wires $W1$ and $W2$ placed in parallel as shown in the figure, carry currents $I$ and $2I$, respectively, in opposite directions. If the two wires are separated by a distance of $4r$, then the magnitude of the magnetic field $\overrightarrow{B}$ between the wires at a distance $r$ ... $\frac{5\mu_{0}I}{6\pi r}$ $\frac{\mu_{0}^{2}I^{2}}{2\pi r^{2}}$
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Feb 12, 2019
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Arjun
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gate2019ec
overrightarrow
vectoralgebra
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4
GATE2016154
The electric field of a uniform plane wave traveling along the negative $z$ direction is given by the following equation: ${\overrightarrow {E}^i_w= ( \hat {a}_x+ j\hat {a}_y)E_0e^{jkz}}$ This wave is incident upon a receiving antenna placed at the origin and ... ), $5$dB Circular(clockwise), Linear, $5$dB Circular(clockwise), Linear, $3$dB Circular(anti clockwise), Linear, $3$dB
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Mar 28, 2018
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gate2016ec1
vectoralgebra
overrightarrow
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5
GATE2015125
A vector $\overrightarrow{P}$ is given by $\overrightarrow{P} = x^3y\overrightarrow{a}_x  x^2y^2\overrightarrow{a}_y  x^2 yz \overrightarrow{a}_z$. Which one of the statements is TRUE? $\overrightarrow{P}$ is solenoidal, but ... $\overrightarrow{P}$ is neither solenoidal, nor irrotational $\overrightarrow{P}$ is both solenoidal and irrotational
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Mar 28, 2018
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Milicevic3306
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gate2015ec1
vectoralgebra
engineeringmathematics
overrightarrow
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6
GATE2014454
Gven $\overrightarrow{F} = z \hat{a}_x + x \hat{a}_y + y \hat{a}_z$. If $S$ represents the portion of the sphere $x^2 +y^2+z^2=1$ for $z \geq 0$, then $\int _s \nabla \times \overrightarrow{F} \cdot \overrightarrow{ds}$ is __________.
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Mar 26, 2018
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Milicevic3306
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gate2014ec4
numericalanswers
vectoralgebra
engineeringmathematics
overrightarrow
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7
GATE2014455
If $\overrightarrow{E} = (2y^3 – 3yz^2)\hat{x} – (6xy^23xz^2) \hat{y}+(6xyz) \hat{z}$ is the electric field in a source free region, a valid expression for the electrostatic potential is $xy^3 – yz^2$ $2xy^3xyz^2$ $y^3+xyz^2$ $2xy^33xyz^2$
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Mar 26, 2018
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gate2014ec4
vectoralgebra
engineeringmathematics
overrightarrow
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8
GATE2014354
A region shown below contains a perfect conducting halfspace and air. The surface current $\overrightarrow{K_{s}}$ on the surface of the perfect conductor is $\overrightarrow{K_{s}}= \hat{x}2$ amperes per meter. The tangential $\overrightarrow{H}$ field in the air just ... $\hat{x}2$ amperes per meter $\hat{z}2$ amperes per meter $\hat{z}2$ amperes per meter
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Mar 26, 2018
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gate2014ec3
vectoralgebra
overrightarrow
planes
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9
GATE2014355
Assume that a plane wave in air with an electric field $\overrightarrow{E}= 10\cos ( \omega t3x\sqrt{3}z )\hat{a_{y}}V/m$ is incident on a nonmagnetic dielectric slab of relative permittivity $3$ which covers the region $z > 0$. The angle of transmission in the dielectric slab is _________ degrees.
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Mar 26, 2018
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gate2014ec3
numericalanswers
vectoralgebra
overrightarrow
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10
GATE2014229
If $\overrightarrow {r}= x\hat{a_{x}}+y\hat{a_{y}}+z\hat{a_{z}}$ and $\mid \overrightarrow{r} \mid= r$ , then $\text{div} ( r^{2} \nabla ( \text{ln }r ) )$ = _______ .
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Mar 26, 2018
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gate2014ec2
numericalanswers
vectoralgebra
overrightarrow
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11
GATE2014253
If the electric field of a plane wave is $\overrightarrow{E}(z,t)= \hat{x}3 \cos(\omega tkz+30^{\circ}) – \hat{y} 4 \sin(\omega t – kz+45^{\circ}) (mV/m),$ the polarization state of the plane wave is left elliptical left circular right elliptical right circular
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Mar 26, 2018
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gate2014ec2
vectoralgebra
overrightarrow
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12
GATE201252
An infinitely long uniform solid wire of radius $a$ carries a uniform dc current of density $\overrightarrow{j}$. The magnetic field at a distance $r$ from the center of the wire is proportional to $r$ for $r\lt a$ and $\frac{1}{r^2}$ for $r\gt a$ $0$ for $r\lt a$ and $\frac{1}{r}$ ... $r\lt a$ and $\frac{1}{r}$ for $r\gt a$ $0$ for $r\lt a$ and $\frac{1}{r^2}$ for $r\gt a$
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Mar 25, 2018
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gate2012ec
vectoralgebra
engineeringmathematics
overrightarrow
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13
GATE20125
The electric field of a uniform plane electromagnetic wave in free space, along the positive $x$ direction, is given by $\overrightarrow{E}=10(\hat{a}_y+j\hat{a}_z)e^{j\:25x}$. The frequency and polarization of the wave, respectively, are $1.2\:GHz$ and left circular $4\:Hz$ and left circular $1.2\:GHz$ and right circular $4\:Hz$ and right circular
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Mar 25, 2018
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gate2012ec
vectoralgebra
overrightarrow
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14
GATE201849
A uniform plane wave traveling in free space and having the electric field ... $=1$) as shown in the figure and there is no reflected wave. The relative permittivity (correct to two decimal places) of the dielectric medium is __________.
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Feb 19, 2018
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gatecse
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gate2018ec
numericalanswers
overrightarrow
vectoralgebra
engineeringmathematics
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15
GATE2017 EC2: 28
If the vector function $\overrightarrow{F}=\widehat{a_x}(3yk_1z)+\widehat{a_y}(k_2x2z)\widehat{a_z}(k_3y+z)$ is irrotational, then the values of the constants $k_1$,$k_2$ and $k_3$, respectively, are $0.3, 2.5, 0.5$ $0.0, 3.0, 2.0$ $0.3, 0.33, 0.5$ $4.0, 3.0, 2.0$
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Nov 23, 2017
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Linear Algebra
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admin
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gate2017ec2
vectoranalysis
overrightarrow
engineeringmathematics
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