## College Physics (4th Edition)

$\frac{q}{m} = 8.6\times 10^{-11}~C/kg$
We can find an expression for the gravitational force: $F = \frac{G~m~m}{r^2}$ We can find an expression for the magnitude of the electric force: $F = \frac{k~q~q}{r^2}$ We can equate the two forces to find the ratio $\frac{q}{m}$: $\frac{k~q~q}{r^2} = \frac{G~m~m}{r^2}$ $\frac{q^2}{m^2} = \frac{G}{k}$ $\frac{q}{m} = \sqrt{\frac{G}{k}}$ $\frac{q}{m} = \sqrt{\frac{6.67\times 10^{-11}~N~m^2/kg^2}{9.0\times 10^9~N~m^2/C^2}}$ $\frac{q}{m} = 8.6\times 10^{-11}~C/kg$