Work

Also, note that the work done by the magnetic force is given by

$$\begin{eqnarray*} W &=& \int \vec{F} \cdot d\vec{r}\\ &=& \int \left(q\vec{v}\times \vec{B}\right) \cdot \vec{v}dt\\ &=& 0, \end{eqnarray*}$$

because the cross product of two vectors is always perpendicular to the two you started with. In particular, $\vec{v}\times\vec{B}$ is perpendicular to $\vec{v}$, so their dot product must give zero. This result is fully general as we made no assumptions regarding $v$ or $B$. Thus, the magnetic field never does any work. Though it may change the direction of velocity, it never changes the magnitude. In particular, for constant $B$ problems, we will only have combinations of straight and circular motion (for example, the helix problems Venkat loves so much...)