Walker, Halliday & Resnick — Magnetic Fields: Problem 4

4 An electron follows a helical path in a uniform magnetic field given by $\vec{B} = (20\hat{i} - 50\hat{j} - 30\hat{k}) \text{ mT}$. At time $t = 0$, the electron's velocity is given by $\vec{v} = (40\hat{i} - 30\hat{j} + 50\hat{k}) \text{ m/s}$. (a) What is the angle $\phi$ between $\vec{v}$ and $\vec{B}$? The electron's velocity changes with time. Do (b) its speed and (c) the angle $\phi$ change with time? (d) What is the radius of the helical path?