Solution
The two positive charges produce an electric field along the x-axis. The field is zero at the origin, increases to a maximum at $x = \frac{a}{\sqrt{2}}$, and then decreases as $x \to \infty$.
Since the rod is electrically neutral, it experiences a force due to polarization (induction). The rod develops a dipole moment aligned with the field. In a non-uniform electric field, a dipole experiences a net force:
$$F = p \frac{dE}{dx}$$Neutral matter is generally attracted towards regions of stronger electric field intensity.
- If the rod is placed in the region $0 < x < a/\sqrt{2}$ (where field is increasing), it is pulled away from the origin towards the maximum field.
- If the rod is placed in the region $x > a/\sqrt{2}$ (where field is decreasing), it is pulled towards the maximum field (towards the origin).
Since the problem does not specify the exact location of the rod relative to the field maximum ($a/\sqrt{2}$), we cannot determine if the net force is towards or away from the origin.
Answer: (d) Information is insufficient.