Bouncing off a charged sheet

Classical Mechanics Level 4

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 \(\sigma\) 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 \(30^\circ\) with respect to the vertical. What is \(\sigma\) in \(\mbox{C/m}^2\)?

Details and assumptions

  • The acceleration of gravity is \(-9.8~\mbox{m/s}^2\).
  • \(\frac{1}{4\pi\epsilon_0}=9 \times 10^9~\mbox{N}\,\mbox{m}^2/\mbox{C}^2\).

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