Physics Question from JEE Main 2025 · 24 January, Shift 1

A square loop of sides $a = 1 \, \text{m}$ is held normally in front of a point charge $q = 1 \, \text{C}$, the charge lying on the perpendicular through the centre of the loop at a distance $\frac{a}{2}$ from it. The square is divided into eight equal parts by its two diagonals and by the two lines joining the midpoints of opposite sides, and five of these eight parts are shaded. The flux of the electric field through the shaded region is $\frac{5}{p} \times \frac{1}{\varepsilon_0} \, \text{N m}^2/\text{C}$, where the value of $p$ is _____.