Answer
$\frac{q}{m} = 8.6\times 10^{-11}~C/kg$
Work Step by Step
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 $\frac{q}{m}$:
$\frac{k~q~q}{r^2} = \frac{G~m~m}{r^2}$
$\frac{q^2}{m^2} = \frac{G}{k}$
$\frac{q}{m} = \sqrt{\frac{G}{k}}$
$\frac{q}{m} = \sqrt{\frac{6.67\times 10^{-11}~N~m^2/kg^2}{9.0\times 10^9~N~m^2/C^2}}$
$\frac{q}{m} = 8.6\times 10^{-11}~C/kg$
