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

Step-by-step solution

Let the length of each side of the equilateral triangle be a . Since the total length of the wire is l , we have a = l 3 . The perpendicular distance d from the centroid (center) of the equilateral triangle to any of its sides is given by: d = a 2 3 = l 3 2 3 = l 6 3 The magnetic field at the center due to one side of the triangle can be found using the Biot-Savart law for a finite straight wire: B₁ = ₀ i 4 d ( ₁ + ₂) For an equilateral triangle, the line segments joining the center to the vertices subtend an angle