A long straight horizontal wire AB carries some current. A is to the north of B. Magnetic field below the wire is eastward. If the wire is now held vertically with A above B with the current in the wire flowing the same way as earlier, find the direction of the magnetic field to the north of the wire

PLACEHOLDER ANSWER - the answer is a direction. Take east, north and up as $$\hat{i}$$, $$\hat{j}$$, $$\hat{k}$$. For a current along $$-\hat{j}$$ (from A to B), the field below the wire is along $$-\hat{j} \times (-\hat{k}) = \hat{i}$$, eastward, so the current flows from A to B. With A above B the current flows downward, $$-\hat{k}$$. To the north of the wire the field is along $$-\hat{k} \times \hat{j} = \hat{i}$$, i.e. eastward.