Two long currents carrying thin wires, both with current $I$, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle ' $\theta$ ' with the vertical. If wires have a mass $\mathrm{\lambda }$ per unit length then the value of $\mathrm{I}$ is:
($g=$ gravitational acceleration)

A rectangular loop of sides $10 \mathrm{cm}$ and $5 \mathrm{cm}$, carrying a current $I$ of $12 \mathrm{A}$, is placed in different orientations as shown in the figure below.
(a)  (b)

(c)  (d)

If there is a uniform magnetic field of $0.3 \mathrm{T}$ in the positive $z$ direction, in which orientations the loop would be in $\left(\mathrm{i}\right)$ stable equilibrium and $\left(\mathrm{ii}\right)$ unstable equilibrium?

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, as shown in the figure) in the vicinity of the wire. If the wire subtends an angle $2{\theta }_o$ at the center of the circle (of which it forms an arch) then the tension in the wire is:

A short bar magnet is placed in the magnetic meridian of the earth with North Pole pointing north. Neutral points are found at a distance of $30 \mathrm{cm}$ from the magnet on the East-West line, drawn through the middle point of the magnet. The magnetic moment of the magnet in ${\mathrm{Am}}^2$ is close to:

(Given $\frac{{\mu }_0}{4\pi }={10}^{-7}$ in SI units and $B_H=$ Horizontal component of earth's magnetic field $=3.6\times {10}^{-5}$ Tesla.)

Two long straight parallel wires, carrying (adjustable) currents $I_1$ and $I_2$ , are kept at a distance $d$ apart. If the force $F$ between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the wires attract each other, the graph showing the dependence of $F$, on the product $I_1{I}_2$ , would be: