An electric current i is carried by a wire of length l which is bent into a square. Determine the magnetic field B at the centre.

Step-by-step solution

Let the side length of the square be a . Since the total length of the wire is l , we have 4a = l a = l 4 . The magnetic field at the centre of the square due to one of its sides is given by the formula for a finite straight wire: B₁ = ₀ i 4 d ( ₁ + ₂) The perpendicular distance from the centre to the side is d = a 2 = l 8 . The angles subtended by the ends of the side at the centre are ₁ = ₂ = 45^ . Substituting these values into the formula: B₁ = ₀ i 4 ( l 8 ) ( 45^ + 45^ ) B₁ = 2 ₀ i l ( 1 2 + 1 2 ) = 2 ₀ i l (