$A$ wire is bent as a parabolic curve and kept in the $x-y$ plane. The curve is described by the equation $x^2 = 6y$. The wire carries a current $i = 2 \ A$. If a uniform magnetic field $\vec{B} = 2 \times 10^{-3} \hat{k} \ T$ is applied,the force experienced by the wire is nearly: (in $hat{j} \ N$)

$A$ $100$ turn rectangular coil $ABCD$ (in $xy$-plane) is hung from one arm of a balance (Figure). $A$ mass of $500 \text{ g}$ is added to the other arm to balance the weight of the coil. $A$ current of $4.9 \text{ A}$ passes through the coil and a constant magnetic field of $0.2 \text{ T}$ acting inward (in $xz$-plane) is switched on such that only arm $CD$ of length $1 \text{ cm}$ lies in the field. How much additional mass '$m$' must be added to regain the balance?

Two thin long parallel wires,separated by a distance $d$,carry a current of $I$ $A$ in the same direction. They will:

$A$ wire $X$ of length $50 \; cm$ carrying a current of $2 \; A$ is placed parallel to a long wire $Y$ of length $5 \; m$. The wire $Y$ carries a current of $3 \; A$. The distance between the two wires is $5 \; cm$ and the currents flow in the same direction. The force acting on the wire $X$ due to wire $Y$ is:

$A$ current of $10 \ A$ flows through two long parallel wires. The magnetic force per unit length on each wire is $2 \times 10^{-3} \ N/m$. If their currents are doubled and the separation between them is halved,then the magnetic force per unit length of each wire becomes $...... \times 10^{-3} \ N/m$.

$A$ fixed horizontal wire carries a current of $200\, A$. Another wire having a mass per unit length of $10^{-2}\, kg/m$ is placed below the first wire at a distance of $2\, cm$ and parallel to it. How much current must be passed through the second wire if it floats in air without any support? What should be the direction of current in it?