For a current flowing into a circular arc, the magnetic induction at the centre isB=(4πrμ0​i​)θ or B∝iθIn the given problem, the total current is divided into two arcsi∝ resistance of arc 1​∝ length of arc 1​ or iθ​∝ angle subtended at centre (θ)1​= constant ​i.e. magnetic field at centre due to arc AB is equal and opposite to the magnetic field at centre due to arc ACB. Or the net magnetic field at centre is zero.