Question

The wire ABC shown in figure forms an equilateral triangle. Find the magnetic field B at the centre O of the triangle assuming the wire to be uniform. 

Answer 1

Let current 2I enter the circuit.
Since the wire is uniform, the current will be equally divided at point A (as shown in the figure).   

Now,
Magnetic field at P due to wire AB = B (say)
(Perpendicular to the plane in outward direction)

Magnetic field at P due to wire BD = B' (say)
(Perpendicular to the plane in outward direction)

Magnetic field at P due to wire AC = Magnetic field at P due to wire AB = B
(Perpendicular to the plane in inward direction)

Magnetic field at P due to wire CD = Magnetic field at P due to wire BD = B'
(Perpendicular to the plane in inward direction)

∴ Net magnetic field at P = B + B' − B − B' = 0