Bouncing off a charged sheet

A point charge of charge 1 mC and mass 100 g is attached to a non-conducting massless rod of length 10 cm. The other end of the rod is attached to a two-dimensional sheet with uniform charge density σ\sigma and the rod is free to rotate. The sheet is parallel to the y-z plane (i.e. it's a vertical sheet). I lift the point charge so the rod is horizontal and release it. I observe that the point charge achieves its maximum speed when the rod makes an angle of 3030^\circ with respect to the vertical. What is σ\sigma in C/m2\mbox{C/m}^2?

Details and assumptions

  • The acceleration of gravity is 9.8 m/s2-9.8~\mbox{m/s}^2.
  • 14πϵ0=9×109 Nm2/C2\frac{1}{4\pi\epsilon_0}=9 \times 10^9~\mbox{N}\,\mbox{m}^2/\mbox{C}^2.
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