Question #42922

A very large, isolated, thin non-conducting sheet has an initial area $A_0$ at temperature $T_0$ and carries a uniformly distributed total positive charge $Q$. A point particle of mass $m$ and positive charge $q$ is projected from a point near the sheet with an initial speed $v_0$ at an angle $\theta$ ($0 < \theta < \pi/2$) with the normal to the sheet. The maximum perpendicular distance the particle travels from its projection point before turning back is $x_0$. The sheet is then uniformly heated to a temperature $T_0 + \Delta T$. The coefficient of linear thermal expansion of the sheet material is $\alpha$. If the same particle is projected again from the same point with the same initial velocity, what is the new maximum perpendicular distance $x$ it reaches? (Assume $\alpha \Delta T \ll 1$, neglect gravity and edge effects).