The charge on this ring, $dq$, is given by the charge density times the area of the ring. The charge density is $\frac{Q}{\pi R^2}$ and the area of the ring is $2\pi r dr$. Therefore, $dq = \frac{Q}{\pi R^2} \cdot 2\pi r dr = \frac{2Qr}{R^2} dr$.
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