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:

Two very long, straight, and insulated wires are kept at $90°$ angle from each other in $\mathrm{x}\mathrm{y}$ plane as shown in the figure.

These wires carry currents of equal magnitude $I$ , whose direction are shown in the figure. The net magnetic field at point $P$ will be:

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)