$A$ wire carrying a current $I$ is placed inside a uniform magnetic field $\vec{B} = -B_0 \hat{k}$. The shape of the wire is parabolic and has the equation $y = 2x - x^2$. The force on the wire will be:

$A$ straight horizontal long wire carries $30 \ A$ current. The linear mass density of the wire is $45 \ g/m$. What is the magnitude of the magnetic field needed to balance the wire in air?

$A$ metallic rod of mass per unit length $0.5\; kg\; m^{-1}$ is lying horizontally on a smooth inclined plane which makes an angle of $30^{\circ}$ with the horizontal. The rod is prevented from sliding down by passing a current through it,while a magnetic field of induction $0.25\; T$ acts on it in the vertical direction. The current flowing in the rod to keep it stationary is: (in $; A$)

An arrangement of three parallel wires placed perpendicular to the plane of the paper,each carrying the same current $I$ in the same direction,is shown in the figure. The magnitude of the force per unit length on the middle wire $B$ is given by:

Two long parallel wires are at a distance of $1 \ m$. Both of them carry $1 \ A$ of current. The force of attraction per unit length between the two wires is

Two parallel wires in free space are $10\, cm$ apart and each carries a current of $10\, A$ in the same direction. The force one wire exerts on the other per metre of length is