Part $(2)$: ${B_2} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{\pi \,i}}{{(a/2)}} \otimes $(along $-Z-$axis)

Part $(3)$: ${B_3} = \frac{{{\mu _0}}}{{4\pi }}.\frac{i}{{(a/2)}}\left( \downarrow \right)$(along $-Y-$axis)

Part $(4)$: ${B_4} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{\pi i}}{{(3a/2)}}\odot$(along $+Z-$axis)

Part $(5)$: ${B_5} = \frac{{{\mu _0}}}{{4\pi }}.\frac{i}{{(3a/2)}}\left( \downarrow \right)$(along -$Y$ $-$ axis) ${B_2} - {B_4} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{\pi i}}{a}\left( {2 - \frac{2}{3}} \right) = \frac{{{\mu _0}i}}{{3a}} \otimes $(along -$Z$ $-$ axis) ${B_3} + {B_5} = \frac{{{\mu _0}}}{{4\pi }}.\frac{1}{a}\left( {2 + \frac{2}{3}} \right) = \frac{{8{\mu _0}i}}{{12\pi a}}\left( \downarrow \right)$ (along -$Y$$ -$ axis)

Hence net magnetic field ${B_{net}} = \sqrt {{{({B_2} - {B_4})}^2} + {{({B_3} + {B_5})}^2}} $$ = \frac{{{\mu _0}i}}{{3\pi a}}\sqrt {{\pi ^2} + 4} $