An equilateral triangle is formed by the wire ABC as shown in the figure. Assuming the wire to be uniform, determine the magnetic field B at the centre O of the triangle.

Step-by-step solution

Let the total current entering at vertex A be I . The current leaves from the midpoint M of the side BC . The current divides into two parallel paths: path A B M and path A C M . Since the wire is uniform, the resistance of each path is proportional to its length. The length of path ABM is L + L/2 = 3L/2 , and the length of path ACM is L + L/2 = 3L/2 . As the lengths and resistances of both paths are equal, the current splits equally. The current in branch ABM is I/2 and the current in branch ACM is I/2 . Let d be