Mumbai university > Electronics and telecommunication engineering, Electronics engineering > Sem 3 > Applied mathematics 3

Marks : 05

Years : MAY 2016

For Irrational $\bigtriangledown \times \bar F=\bar 0$

$\bigtriangledown \times \bar F =\begin{vmatrix} \bar i & \bar j& \bar k \\ \dfrac d{dx}&\dfrac d{dy}& \dfrac d{dz}\\ (y^2-z^2+3yz-2x) & (3xz+2xy) & (3xy-2xz+2z) \\ \end{vmatrix} $

$=\bar i [3x-3x]- \bar j[(3y-2z) -(-2z+3y)]+\bar k [(3z+2y)-(2y+3z)] \\ =\bar 0 \\ \Rightarrow \bar F \text { is irratational.} $

For Solenoidal $\bigtriangledown \times \bar F=0 \\ \bigtriangledown \times \bar F= \dfrac {dF_1}{dx} + \dfrac {dF_2}{dy}+\dfrac {dF_3}{dz} =(-2)+(2x)+(-2x+2)=0 $

$\Rightarrow \bar F $ is also solenoidal