# Charged Ring Rolling!

**Electricity and Magnetism**Level 4

A non-conducting ring of mass \(m\) and radius \(R\), the charge per unit length \(\lambda\) is shown in figure. It is then placed on a rough non-conducting horizontal plane. At time \(t=0\), a uniform electric field \(\vec{E} = E_0 \hat{i}\) is switched on and the ring starts rolling without sliding. Find the frictional force \((f)\)acting on the ring.

Given - \( |E_0| = 3 , R = 4m , |\lambda| = 6 \)

Find the value of \(\sqrt{\frac{f}{2R}}\).