GATE 2014 EC (EC3) – Question 63
$\mathbf A=(\cos x)(\sin y)\hat a_x+(\sin x)(\cos y)\hat a_y$. Find $|\nabla\times\mathbf A|$.
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Correct answer: -0.01 to 0.01
Explanation
The only possible curl component is along z:∂Ay/∂x−∂Ax/∂y. Both derivatives equal cosxcosy because Ay=sinxcosy and Ax=cosxsiny. Their difference is zero, and there are no z-dependent components. Thus the curl vector and its magnitude are **0**.