Consider a uniform electric field of magnitude E0 pointing in the -ĵ direction. As we will see later in this course, one way to create such a field is to use two very large and oppositely charged plates. The plates are contained in the (x,z) plane, are of length L in the î direction, and are separated by a distance 2d (the dimension in the k̂ direction is irrelevant in this problem). A point particle of mass m and positive charge q is initially outside the gap between the two plates moving along the +x axis with an speed v0. The particle enters the region of uniform electric field at the midpoint between the two plates.
Calculate the minimum speed v0 needed for the particle not to hit the lower plate. Express your answer in terms of q, m, L, d, and E0.