The direction of the magnetic field created by the current in conductor AB depends on the direction of the current itself. If we assume the current flows from left to right (which is a common convention if the positive terminal of the power source is on the left), then using the right-hand rule, the magnetic field around the conductor would be directed out of the page on the right side of the conductor and into the page on the left side of the conductor. However, without knowing the current's direction, the magnetic field's direction cannot be definitively stated. The image does not provide enough information to determine this.
Answer: The direction of the magnetic field cannot be determined without knowing the direction of the current.