a
(a) Magnetic field due to one side of the square at centre \(O\)
\({B_1} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2i\sin {{45}^o}}}{{a/2}}\)

\(==>\) \({B_1} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\sqrt 2 \,i}}{a}\)
Hence magnetic field at centre due to all side
\(B = 4{B_1} = \frac{{{\mu _0}(2\sqrt 2 i)}}{{\pi a}}\)
Magnetic field due to \(n\) \(turns\)
\({B_{net}} = nB = \frac{{{\mu _0}2\sqrt 2 ni}}{{\pi a}} = \frac{{{\mu _0}2\sqrt 2 ni}}{{\pi (2l)}}\)\( = \frac{{\sqrt 2 {\mu _0}ni}}{{\pi l}}\)