A vertical wire carries current upward. A positively charged particle located east of the wire has a velocity directed a) upward b) westward. In each of the cases find the direction of the force on the wire.

PLACEHOLDER ANSWER - the answer is two directions. Take east, north and up as $$\hat{i}$$, $$\hat{j}$$, $$\hat{k}$$; for current along $$\hat{k}$$ the field east of the wire is along $$\hat{k} \times \hat{i} = \hat{j}$$, northward. Using $$\vec{F} = q\vec{v} \times \vec{B}$$, for upward velocity the force on the particle is along $$\hat{k} \times \hat{j} = -\hat{i}$$ (west), and for westward velocity it is along $$-\hat{i} \times \hat{j} = -\hat{k}$$ (downward). By Newton's third law the force on the wire is opposite, so it is a) eastward and b) upward.