The current flows into the circular coil and using the KCL, splits equally between the two arms because both the arms are equal in length and ae made up of the same material.

Hence the current in the upper section as well as the lower section will be i/2.

The current leaves the loop again and the resultant current leaving the coil will again be i.

The magnitude of the current is same and the direction is opposite at every point of time. Magnetic fields produced will hence also be zero as both the arms produce equivalent magnetic field which neutralize each other. Hence net magnetic field at the center will be 0