Figure shows a massless wheel of radius R and massless spokes with five charges each of charge as shown and mass m. System is placed in a field created by two large fixed plates having charges $+ Q_{0}$ and $- Q_{0},$ respectively. Entire assembly lies in a smooth horizontal plane. Wheel is placed in horizontal plane and constrained to move in horizontal plane. Initially spokes are released along x & y axis as shown in figure. (A = surface area of plate)
The instantaneous angular acceleration of the ring is $α = \frac{Q Q_{0}}{n m A R \in_{0}}$ when $n =$

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Detailed Solution

$α = \frac{τ}{I} = \frac{F . R + F . R}{I} = \frac{2 F R}{I} = \frac{2 (\frac{Q Q_{0}}{A \in_{0}}) R}{4 m R^{2}}$

$\Rightarrow α = \frac{Q Q_{0}}{2 m A R \in_{0}}$

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