 Basics - Grad Plus

### Electronics & Comm. Engineering (EC) | Topic-wise Previous Solved GATE Papers | Electromagnetics

Solutions for previous GATE-EC questions of Electromagnetics (Basics)
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Solutions for previous GATE-EC questions of Electromagnetics (Magnetic Fields)
Solutions for previous GATE-EC questions of Electromagnetics (Uniform Plane Waves)
Solutions for previous GATE-EC questions of Electromagnetics (Transmission Lines)
Solutions for previous GATE-EC questions of Electromagnetics (Waveguides)
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# Basics

Q.  [1994 1M]

Ans:- \nabla\times\overrightarrow A

Exp- Using Stoke’s theorem

Q. If a vector field is related to another vector field through ,Which of the following is true? Note: C and SC refer to any closed counter and any surface whose boundary is C. [2009 2M]

a) $\oint_C\overrightarrow V\cdot\overrightarrow{dl}=\int\limits_{S_C}\int\overrightarrow A\cdot\overrightarrow{ds}$

b) $\oint_C\overrightarrow A\cdot\overrightarrow{dl}=\int\limits_{S_C}\int\overrightarrow V\cdot\overrightarrow{ds}$

c) $\oint_C\nabla\times\overrightarrow V\overrightarrow{dl}=\int\limits_{S_C}\int\nabla\times\overrightarrow A\cdot\overrightarrow{ds}$

d) $\oint_C\nabla\times\overrightarrow A\cdot\overrightarrow{dl}=\int\limits_{S_C}\int\overrightarrow V\cdot\overrightarrow{ds}$

Ans-(b)

Exp- Stoke’s theorem

Q. Consider a closed surface S surrounding a volume V. If is the position vector of a point inside s, with the unit normal on S,the value of the integral [2011 1M]

a) 3 V

b) 5 V

c) 10 V

d) 15 V

Ans-(d)

Exp- For close surface, we can use Divergence Theorem.

\oint_s\overrightarrow A\cdot\overrightarrow{ds}=\int_v\left(\nabla\cdot\overrightarrow A\right)dv

Q. The direction of vector A is radially outward from the origin,with where and K is a constant. The value of n for which is [2012 2M]

a) -2

b) 2

c) 1

d) 0

Ans- (a)

Exp- $\left|A\right|=Kr^n$

For \nabla\cdot\overline A to be zero, derivative must be zero in other words (rn+2) must be constant.

This could be possible only if n = -2.

Q. A vector is given by

Which of the following statements is True? [2015 1M,set-2]

a) $\overrightarrow P$ is solenoidal,but not irrotational

b) $\overrightarrow P$ is irrotational,but not solensoidal

c) $\overrightarrow P$ is neither solenoidal nor irrotational

d) $\overrightarrow P$ is both solenoidal and irrotational

Ans-(a)

Exp- $\overrightarrow P=x^3y{\overrightarrow a}_x-x^2y^2{\overrightarrow a}_yx^2yz{\overrightarrow a}_z$

For solenoidal, $\nabla\cdot\overrightarrow P=0$ $\Rightarrow\overrightarrow P$ is solenoidal

For irrotational, $\nabla\times\overrightarrow P=0$

\begin{array}{l}={\overrightarrow a}_x\left(-x^2z\right)+{\overrightarrow a}_y\left(2xyz\right)+{\overrightarrow a}_z\left(-2x^2-x^3\right)\\\neq0\\\Rightarrow\overrightarrow P\;is\;not\;irrotational\end{array}

Q. If the vector function

is irrotational,then the values of the constants respectively,are[2017 2M Set-2]

a) $0.3,-2.5,0.5$

b) $0.0,3.0,2.0$

c) $0.3,0.33,0.5$

d) $4.0,3.0,2.0$

Ans-(b)

Exp- $\overrightarrow F={\widehat a}_x\left(3y-k_1z\right)+{\widehat a}_y\left(k_2x-2z\right)-{\widehat a}_z\left(k_3y+z\right)$

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