Answer:
[tex]B_{net} = \frac{2\sqrt2 \mu_0 i}{\pi d}[/tex]
Explanation:
Magnetic field due to straight current carrying wire is given by the formula
[tex]B = \frac{\mu_0 i}{4\pi r}(sin\theta_1 + sin\theta_2)[/tex]
now we will have for one side of the square at its center position given as
[tex]B = \frac{\mu_0 i}{4\pi (\frac{d}{2})}(sin45 + sin45)[/tex]
[tex]B = \frac{2\sqrt2 \mu_0 i}{4 \pi d}[/tex]
now for the we have for complete square loop it will become 4 times of the one side
[tex]B_{net} = 4 B[/tex]
[tex]B_{net} = 4 \frac{2\sqrt2 \mu_0 i}{4 \pi d}[/tex]
[tex]B_{net} = \frac{2\sqrt2 \mu_0 i}{\pi d}[/tex]
