# A conducting wire bent in the form of a parabola $y^2 = 2x$ for $0 \leq x \leq 2$, carries a current $i = 1A$ in anti- clockwise direction as looked from above the $x-y$ plane. There exists uniform magnetic field $-2 \hat k$ Tesla in the region. The magnetic force on the wire is

$\begin {array} {1 1} (a)\;-16\hat i & \quad (b)\;-8 \hat i \\ (c)\;16\hat i & \quad (d)\;8\hat i \end {array}$

The force on the wire is equivalent to the force experienced by an imaginary wire
joining the end points of the parabolic wire $\because$ the net force on a closed loop is zero
$F = B i \ell$
$\ell = 4$
$F = 8$
Ans : (d)