A long conductor carries a current northward. A moving positively charged particle is located vertically below the conductor. Find the force acting on it if its velocity is directed (i) downward (ii) westward

PLACEHOLDER ANSWER - the answer is two directions. Take east, north and up as $$\hat{i}$$, $$\hat{j}$$, $$\hat{k}$$; below a northward current the field is along $$\hat{j} \times (-\hat{k}) = -\hat{i}$$, westward. (i) For a downward velocity the force is along $$-\hat{k} \times -\hat{i} = \hat{j}$$, northward. (ii) For a westward velocity the velocity is parallel to the field, so there is no force.