E $\times$B drift

(D. R. Nicholson ~ 2.3) Consider a particle moving in a time-dependent electric field $\vec{E} = - \dot{E} t\vec{u}_y$, where $\dot{E}$ is a constant, and a uniform magnetic field $\vec{B}=B_0\vec{u}_z$.

(a) Calculate the $\vec{E}\times\vec{B}$ drift.

(b) Relate the resulting accelerated drift with a force and verify that the drift due to that force is the polarization drift.