Question #42662

A trolley moves along the horizontal $+x$-axis with a constant acceleration $a = \frac{3g}{4}$. Inside the trolley, a uniform electric field $\vec{E} = \frac{mg}{q} \hat{i} + \frac{mg}{2q} \hat{j}$ is maintained. A straight, rigid, frictionless dielectric wire of length $L$ is fixed inside the trolley. The ends of the wire are at coordinates $A \left(0, \frac{4L}{5}\right)$ and $B \left(\frac{3L}{5}, 0\right)$ with respect to a coordinate system fixed to the trolley, where the $y$-axis is vertically upwards. A small bead of mass $m$ and charge $+q$ is released from rest at point $A$. What is the kinetic energy of the bead when it reaches point $B$, as measured in the trolley's reference frame?