An infinite uniform current carrying wire is kept along z-axis, carrying current I₀ in the direction of the positive z-axis. OABCDEFG represents a circle (where all the points are equally spaced), whose centre at point (4m, 0m) and radius 4 m as shown in the figure. If ${\int }_{\mathrm{DEF}} \overrightarrow{\mathrm{B}}\cdot \overrightarrow{\mathrm{d}}\mathrm{\ell }=\frac{{\mathrm{\mu }}_0{\mathrm{I}}_0}{\mathrm{k}}$in S.I. unit, then the value of k is