A square wire of each side l carries a current I . The magnetic field at the mid-point of the square

Step-by-step solution

Magnetic field due to a finite wire at perpendicular distance d is B = ₀ I 4 d ( ₁ + ₂) , where ₁ and ₂ are angles subtended by the ends of the wire at the point. For the center of the square, perpendicular distance from center to each side is d = l 2 , and ₁ = ₂ = 45° . Field due to one side: B₁ = ₀ I 4 l 2 ( 45° + 45°) = 2 ₀ I 4 l 2 2 = 2 2 ₀ 4 I l By right-hand rule, all four sides produce field in the same direction at the center. B_ total = 4 B₁ = 8 2 ₀ 4 I l