Question

A thin rigid insulated rod of mass m and length l carrying a charge Q unformly distrivuted along its length is smoothly pivoted at P. It is palced in between the charged large conducting plates. Disregard gravity.
(a) Find the initial accelaeration of the rod.
(b) Find the angular speed of the rod as the function of angel `theta` of rotation `omega=f(theta)`, if the rod is allowed to rotate freely .

Answer 1

Correct Answer - (a)`(3Q sigma)/(2ml epsilon_(0))` (b) `sqrt((3Q sigma sin theta)/(epsilon_(0)ml))`
(a) `F=QE=(Q sigma)/(epsilon_(0))`
,
(b) Work done by F=KE gained by the rod
or, `F(l)/(2) sin theta=(1)/(2)(Ml^(2))/(3)omega^(2)`
or `omega=sqrt((3F sin theta)/(ml))=sqrt((3Q sigma sin theta)/(epsilon_(0)ml))`.