E \(\times\)B drift

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(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.