Question

A large sheet carries uniform surface charge density sigma.A rod of length 2l has a linear charge density lamda on one half and -lama on the other.The rod is hinged at mid point O and makes theta with normal to the sheet.The torque experienced by the rod is

Answer 1

The torque experienced by the rod will be calculated by the following:

           Force on elementary length. = Eλdx,

          Torque=Eλdxxsinθ

          Now,

           Integrating from 0 to l, we get, λEsinθl2/2

          Again, for lower part (-λ)

          Torque in same sense. λEsinθl2/2

          So net torque = λEsinθl2 E=σ/2ε0

          Thus, τ= λEsinθl2/2ε0