Two long current 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 mass $\lambda$ per unit length then the value of $I$ 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 figures below:

$\left(\mathrm{a}\right)$  $\left(\mathrm{b}\right)$ 

$\left(\mathrm{c}\right)$ $\left(\mathrm{d}\right)$ 

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?

An infinitely long, current-carrying wire and a small current-carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is $d\left(d\gg a\right)$. If the loop applies a force $F$ on the wire then

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of $10 \mathrm{A}$. The magnetic field at point $O$ will be close to