To maintain the compass needle’s orientation without deflection, the current-carrying conductor should be placed in a plane perpendicular to the compass needle’s plane. The deflection will be maximum when the conductor is parallel to the magnetic field lines at point A, which in this case is when the conductor is in the plane of the paper.
Explanation:
No Change in Deflection:
A current-carrying conductor generates a magnetic field. To avoid changing the compass needle’s orientation, the magnetic field produced by the conductor needs to either be perpendicular to the compass needle’s plane or cancel out the earth’s magnetic field at point A. Placing the conductor perpendicular to the compass needle’s plane ensures the conductor’s magnetic field is only in a direction perpendicular to the compass needle’s axis of rotation, preventing it from being deflected.
Maximum Deflection:
The magnetic field produced by a current-carrying conductor is strongest when the observation point is closest to the wire. When the conductor is in the plane of the paper, its magnetic field is strongest in the plane of the paper, leading to maximum deflection of the compass needle.