Question

A vector field is given as $F(x, y) = (100x + 100y) i + (−50x + 200y) j$, where $i$ and $j$ are the unit vectors along the $x$ and $y$ axes in the Cartesian frame, respectively. Then the value of
$∮F(x, y). dl$
where $dl = dx i + dy j$ is an elemental path taken over an anticlockwise circular contour $C$ of radius $r = 2$ is

• A. $-100\pi$
• B. $-800\pi$
• C. $-400\pi$
• D. $400\pi$

Answer 1

Answer: (B)

$-800\pi$

Answer 2

The correct option is (B): $-800\pi$.