A positively charged particle to the east of a long vertical current carrying wire having a velocity directed eastward experiences a vertical upward force. Find the direction of the force on a positively charged particle located south of the conductor and having a velocity directed vertically upward.

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