Chapter 23 - Gauss' Law - Problems - Page 683: 63

$q=-1.04nC$

$F_e=F_c$ Where $F_e$ is electrostatic force and $F_c$ is centripetal force $\implies \frac{qe}{4\pi \epsilon_{\circ}r^2}=\frac{mv^2}{r}$ $q=\frac{mv^2({4\pi \epsilon_{\circ}r^)}}{e}$ Putting the values, we get $q=\frac{1.67\times10^{-27}(3\times10^5)^2(4\pi\times8.85\times10^{-12}\times0.01)}{1.602\times10^{-19}}$ $q=-1.04\times10^{-19}C=-1.04nC$