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.}
