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 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∘ with respect to the vertical. What is σ in C/m2?

Question

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 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∘ with respect to the vertical. What is σ in C/m2?
Details and assumptions
•	The acceleration of gravity is −9.8 m/s2.
•	14πϵ0=9×109 Nm2/C2.

Sigma · Answer

You need to use the idea the the change in potential energy is equal to the change in kinetic energy