A horizontal conductor is oriented north south and carries some current. A positively charged particle located vertically above it and having a velocity directed northward experiences an upward force. What is the direction of the force if this charged particle were located to the east of the conductor and had a velocity directed towards the conductor.

PLACEHOLDER ANSWER - the answer is a direction. Take east, north and up as $$\hat{i}$$, $$\hat{j}$$, $$\hat{k}$$. An upward force on a northward velocity needs $$\vec{B}$$ westward above the wire ($$\hat{j} \times (-\hat{i}) = \hat{k}$$), which happens when the current flows south. East of a southward current the field is along $$(-\hat{j}) \times \hat{i} = \hat{k}$$, upward. For a velocity towards the conductor (westward), the force is along $$(-\hat{i}) \times \hat{k} = \hat{j}$$, i.e. northward.