An alpha particle moving vertically downward at right angles to a uniform magnetic field experiences a northward force. What is the direction of the force on a beta particle moving northward?

PLACEHOLDER ANSWER - the answer is a direction. Take east, north and up as $$\hat{i}$$, $$\hat{j}$$, $$\hat{k}$$. For the positive alpha particle, $$-\hat{k} \times \vec{B}$$ is along $$\hat{j}$$, which needs $$\vec{B}$$ along $$-\hat{i}$$ (westward). For the negative beta particle moving along $$\hat{j}$$, the force is along $$-\left(\hat{j} \times -\hat{i}\right) = -\hat{k}$$, i.e. vertically downward.