Earth's magnetic field is due to:

A particle with charge $q$, moving with a momentum $p$ enters a uniform magnetic field normally. The magnetic field has magnitude $B$ and is confined to a region of width $d$, where $d<\frac{p}{Bq},$ The particle is deflected by an angle $\theta$ in crossing the field

To which of the following quantities, the radius of the circular path of a charged particle moving at right angles to a uniform magnetic field is directly proportional?

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)