A large sheet carries uniform surface charge density `sigma`. A rod of length `2l` has a linear charge density `lamda` on one half and `-lamda` on the second half. The rod is hinged at mid-point O and makes an angle `theta` with the normal to the sheet. The maximum torque experienced by the rod is (if `theta` is variable) :

Options

A. 0
B. `(sigmalamdal^(2))/(2epsilon_(0))sintheta`
C. `(sigmalamdal^(2))/(epsilon_(0))sintheta`
D. `(sigmalamdal)/(2epsilon_(0))`

Answer

D

Explanation

Charge on element `d_q=lamda dx`
Force on element `d_F=lamda dxE`
Torque on element `d_T= lamda d x E x sin theta`
Torque on rod `=-2 int_0^l lamda E sin theta x dx`
`=2 lamda E sin theta .l^2/2= lamda E sin thetal^2=(lamda sigma sin theta l^2)/(2e_0)`