5. Circular Motion in Uniform B A particle of charge $q$ and mass $m$ is in a uniform magnetic field $\vec{B} = B_0 \hat{z}$. The particle, initially at the origin, is given a momentum of magnitude $p_0$. What must be the direction of the momentum if the particle is to reach the point $(a, 0, 0)$ (where $a < 2p_0/qB$) in the least possible time? What is this time? {Hints: “least possible time” is not an indication to take a derivative to find a minimum; rather, there are two possible answers, you choose the shorter time. Also, this problem involves rather little E&M – it's more about geometry and kinematics.}