Two long parallel wires in the $yz$ plane at a distance $2\mathrm{a}$ apart carry a steady current $I$ in opposite directions. Midway between the wires is a rectangular loop of wire $2b\times d$ carrying current $I$ as shown in the figure $\left(b<a<2b\right)$. The loop is free to rotate about the $z$ axis and the currents remain fixed to $I$ irrespective of the relative motion between the loop and the wire

Take $a=8\mathrm{cm},b=6\mathrm{cm}$ and $d=5\mathrm{cm}$ also let $I=1\mathrm{A}$

Torque tending to rotate the rectangular loop about its axis when $\varphi =90°$ is $x\times {10}^{-7}\mathrm{Nxcm}$. Find $x$

Two magnetic dipoles $\mathrm{X}$ and $\mathrm{Y}$ are placed at a separation $\mathrm{d}$ , with their axes perpendicular to each other. The dipole moment of $\mathrm{Y}$ is twice that of $\mathrm{X}$ . A particle of charge $\mathrm{q}$ is passing through their mid-point $\mathrm{P}$ , at angle $\mathrm{\theta }={45}^{\mathrm{o}}$ with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant? ( $\mathrm{d}$ is much larger than the dimension of the dipole)

Consider a negatively charged particle moving with a velocity $v$ in a magnetic field $B$ applied perpendicular to the plane of the paper (into the paper). The particle follows the path $A$ or $B$ or $C$ or $D$ (shown in the figure)

An electron enters a magnetic field of $\left(3 \hat{i}+4 \hat{j}\right) \mathrm{T}$ with a velocity of $\left(6 \hat{j}+4 \hat{k}\right) \mathrm{m} {\mathrm{s}}^{-1}.$ The acceleration produced is

($\frac{e}{m}$ of electron $=1.76\times {10}^{11} \mathrm{C} {\mathrm{kg}}^{-1}$)

A particle with charge $q$ moves with a velocity $v$ in a direction perpendicular to the directions of uniform electric and magnetic fields, $E$ and $B$ respectively, which are mutually perpendicular to each other. Which one of the following gives the condition for which the particle moves undeflected in its original trajectory?

An electric current $I$ enters and leaves a uniform circular wire of radius $r$ through diametrically opposite points. A particle carrying a charge $q$ moves along the axis of the circular wire with speed $v$. What is the magnetic force experienced by the particle when it passes through the centre of the circle?