Question

find the magnetic field at the centre of a square of side l carrying current I

Answer 1

I think the easiest way would be to try to solve the problem of finding the magnetic field produced by a straight current-carrying piece of wire of length L. Try to find the field at a point a distance x from the wire on its perpendicular bisector. You can do this by splitting the wire into infinitessimal lengths dl and then use the Biot and Savart law to calculate the field produced by dl. Then integrate along the length of the wire to find the total. I think you should get B = μ 0 I 4 π L x √ x 2 + ( L / 2 ) 2 . B=μ0I4πLxx2+(L/2)2. Now you've done the hard part it's just a matter of adding the fields from each of the 4 sides of the loop.

Reference https://www.physicsforums.com/threads/finding-the-magnitude-of-a-magnetic-field-from-a-square-loop.517337/