Past GATE Paper 2009 EC Electromagnetic Question's Solution

# GATE EC 2009 Electromagnetics Solution

If a vector field $\overrightarrow V$ is related to another vector field $\overrightarrow A$ through $\overrightarrow V=\nabla\times\overrightarrow A$ Which of the following is true? Note: C and SC refer to any closed counter and any surface whose boundary is C.

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

Explanation

Stoke’s theorem

$\oint_C\overline A\cdot\overline{dl}=\iint_S\left(\nabla\times\overrightarrow A\right)\cdot\overline{ds}=\iint_S\overline V\cdot\overline{ds}$

This is a solution for the Past GATE Paper 2009 question of Electromagnetics is presented from our course Electronics & Comm. Engineering (EC) | Topic-wise Previous Solved GATE Papers | Electromagnetics

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