Two magnetic dipoles, \(X\) and \(Y,\) are separated by a distance \(d,\) with their axes oriented perpendicular to each other. The dipole moment of \(Y\) is twice that of \(X.\) A charged particle with charge \(q\) moves with velocity \(v\) through their midpoint \(P,\) which makes an angle \(\theta=45^\circ\) with the horizontal axis, as shown in the diagram. Assuming \(d\) is much larger than the dimensions of the dipoles, the magnitude of the force acting on the charged particle at this instant is:

A small bar magnet placed with its axis at \(30^\circ\) with an external field of \(0.06\) T experiences a torque of \(0.018\) Nm. the minimum work required to rotate it from its stable to unstable equilibrium position is:
1. \(7.2\times 10^{-2}~\text{J}\)
2. \(11.7\times 10^{-3}~\text{J}\)
3. \(9.2\times 10^{-3}~\text{J}\)
4. \(6.4\times 10^{-2}~\text{J}\)