A non-conducting ring of mass m and radius R is charged as shown. The charge density, i.e. charge per unit length is `lamda`. It is then placed on a rough non-conducting horizontal plane. At time `t = 0`, a uniform electric field `E = E_0hati` is switched on and the ring starts rolling without sliding. Determine the friction force (magnitude and direction) acting on the ring when it starts moving.

Answer

`2 lambdaRE_(0) hat(i)`

Explanation

`underset(pi/2)overset(0)(int)2(lambdaRd theta)xxE_(0)R cos theta=FxxR`
`2lambdaR^(2)E_(0)underset(0)overset(pi/2)(int)cos theta d theta=2lambdaR^(2)E_(0)=FR`
`rArr F=2lambdaRE_(0)`