An infinitely large, nonconducting plane carries a uniform positive surface charge density \(+\sigma\) and has a small hole drilled through its center. A small particle with positive charge \(+q\) is launched from point \(P_1\), located at a distance \(d\) to the left of the plane, passes through the hole along a straight path perpendicular to the plane, and reaches point \(P_2\), located at a distance \(2d\) to the right of the plane. What is the change in the electric potential energy \(\Delta U = U_2 - U_1\) of the particle-plane system as the particle moves from point \(P_1\) to point \(P_2\)?