calculate the magnetic filed at the center of a square current loop of side a

We know the sides of square are at right angles, draw a perpendicular bisector through 2 adjacent corners and you will get 45°angle. Draw another perpendicular bisector of that side enclosed in the triangle you have got and calculate it's length (tan theta= prerpendicular/ a/2) you will get it a/2 …

Magnetic field due to one side of square will be μ•i(cos45°-cos45°)/4πa

B=μ•i/√2πa (inside the plane of paper)

Directions and magnitude of magnetic field of all sides is same so you just need to add up the magnetic field...

B_total=4× μ•i/√2πa

Btotal = 2√2μ•iπa....

Hope it clears!!!!

Thank you!!!