$A$ horizontal wire carries $160 \ A$ current. Below it,another wire with a linear mass density of $10 \ g \ m^{-1}$ is kept at a distance of $4 \ cm$. If the lower wire hangs in the air,what is the current in this wire when the direction of current in both wires is the same (in $A$)? $(g=10 \ m \ s^{-2} \text{ and } \mu_0=4 \pi \times 10^{-7} \ T \ m \ A^{-1})$

Two long wires with no contact are placed perpendicular to each other. $i_1$ and $i_2$ are currents flowing through these wires respectively. The magnetic force on a small length '$d$' of the second wire situated at a distance '$l$' from the first wire is proportional to,

$A$ wire carrying current $I$ is tied between points $P$ and $Q$ and is in the shape of a circular arc of radius $R$ due to a uniform magnetic field $B$ (perpendicular to the plane of the paper,shown by $\times \times \times $) in the vicinity of the wire. If the wire subtends an angle $2\theta_0$ at the centre of the circle (of which it forms an arc),then the tension in the wire is:

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by $15 \ cm$ length of wire $Q$ is . . . . . . . $(\mu_0 = 4 \pi \times 10^{-7} \ T \cdot m/A)$

Obtain the expression for the force between two parallel current-carrying wires.

$A$ conductor lies along the $z$-axis in the range $-1.5 \le z < 1.5 \ m$ and carries a fixed current of $10.0 \ A$ in the $-\hat{a}_z$ direction (see figure). For a magnetic field $\vec{B} = 3.0 \times 10^{-4} e^{-0.2x} \hat{a}_y \ T$,find the power required to move the conductor at a constant speed to $x = 2.0 \ m, y = 0 \ m$ in $5 \times 10^{-3} \ s$. Assume parallel motion along the $x$-axis.