A long horizontal conductor carries a current eastward. A moving positively charged particle is located vertically above the conductor at a given moment. Find the direction of the force acting on it if its velocity is directed (i) downward (ii) westward (iii) northward

PLACEHOLDER ANSWER - the answer is three directions. Take east, north and up as $$\hat{i}$$, $$\hat{j}$$, $$\hat{k}$$; for a current along $$\hat{i}$$ the field above the wire is along $$\hat{i} \times \hat{k} = -\hat{j}$$, i.e. southward. Using $$\vec{F} = q\vec{v} \times \vec{B}$$, (i) downward velocity gives $$-\hat{k} \times -\hat{j} = -\hat{i}$$, westward force; (ii) westward velocity gives $$-\hat{i} \times -\hat{j} = \hat{k}$$, upward force; (iii) northward velocity is antiparallel to the field, so there is no force.