Final answer:
The problem involves computing the electric field in a plasma, finding the equation of motion of a charged particle, and determining its kinetic energy. The electric field is determined by using the cross product of the drift velocity and the magnetic field. The particle's motion can be described by the Lorentz force equation, and its kinetic energy is calculated with the mass and velocity.
Step-by-step explanation:
The question describes a charged particle in a plasma with a uniform magnetic field and an electric drift. To find the electric field E in the plasma, we can use the formula that relates the electric field to the magnetic field in the context of a drifting plasma. Since the drift velocity U is given as U = νEx, and the magnetic field B is B0z, the electric field can be found using the equation E = U x B (cross product). Here, the drift is along the x-axis and the magnetic field along the z-axis, hence the electric field will be along the y-axis.
To find the equation of motion x(t), y(t), and z(t), we apply the Lorentz force equation, F = q(E + v x B), where v is the velocity of the particle. Since the particle is released from rest, its initial velocity is zero, and hence the initial acceleration is due to the electric field alone. Over time, as the particle gains velocity perpendicular to the magnetic field, it will start experiencing a magnetic force that will cause it to move in a circular path, superimposed with the drift due to the electric field giving a helical motion.
The kinetic energy K of the particle in the plasma rest frame can be determined by the work-energy theorem. Initially, the particle has zero kinetic energy, but as it accelerates under the influence of the electric and magnetic fields, it gains kinetic energy which can be calculated using K = (1/2)mv2, where v is the velocity of the particle.