Question

A large sheet carries uniform surface charge density `sigma` . A rod of length 2l has a linear charge density `lambda` on one half and `-lambda` on the second half. The rod is hinged at the midpoint O and makes an angle `theta` with the normal to the sheet. The torque experience by the rod is

A. `0`
B. `(sigma lambdal^(2))/(2 varepsilon_(0)) sin theta`
C. `(sigma lambdal^(2))/( varepsilon_(0)) sin theta`
D. `(sigma lambdal)/(2 varepsilon_(0))`

Answer 1

Correct Answer - B
` d tua= 2 int_0^l dF x. sin theta = 2 int _0^l =2 int-0^l E. dq x sin theta`
` = 2 E int _0^l dx sin theta`
` = 2 lambda E sin theta int_0^l x dx = 2 lambda E sin theta. [x^2/2]_0^l`
` =lambda E sinq.l^2 = (sigma lambdal^2)/(2 in_0) sin theta`.