A proton has mass \(m_{p}\) and charge \(+e\). The force it exerts on another proton at a distance \(r\) is given by \(F(r)=\frac{1}{4 \pi \in_{0}} \frac{e^{2}}{r^{2}}\) where \(\frac{1}{4 \pi \epsilon_{0}} \approx 9 \times 10^{9} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{C}^{2}\), and \(e=1.6 \times 10^{-19} \mathrm{C}\). How much work is needed to increase the separation between the protons from \(R\) to \(9 R\) ?