A magnetic compass needle is placed in the plane of paper near point A. In which plane should a straight current-carrying conductor be placed so that it passes through A and there is no change in the deflection of the compass? Under what condition is the deflection maximum and why?

In the plane of the paper itself. The axis of the compass is vertical and the field due to the conductor is also vertical. It could result in a dip of a compass needle which is not possible in this case (dips result only if the axis of the compass is horizontal). The deflection is maximum when the conductor through A is perpendicular to the plane of the paper and the field due to it is maximum in the plane of the paper.

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