A thin non-conducting ring or radius a has a linear charge density `lambda = lambda_(0) sin phi`. A uniform electric field `E_(0) hat(i) + E_(0) hat(j)` exist in the region . .Net torque acting on ring is given as :

Options

A. `E_(0)sqrt2pia^(2)lamda_(0)`
B. `E_(0)pia^(2)lamda_(0)`
C. `2E_(0)pia^(2)lamda_(0)`
D. zero

Answer

D

Explanation

`dq=(lamda_0 sin theta) ad theta`
`dp=dq times 2a=2a lamda_0 sin theta d theta`
Or `d overlinep=2a lamda_0 sin theta d theta [- cos theta hat i- sin theta hat j]`
Now `t= int_0 ^pi doverline p times overlineE`
`=2pi lamda_0 int_0^(pi) (- cos theta sin theta hat i -sin^2 theta hatj) ties (E_0 hatj +E_0 hat j)=E_0 pi a^2 lamda_0`