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  4. Two particles, each of mass m and carrying charges Q, are separated by some distance. If they are in equilibrium under mutual gravitational and electrostatic forces then Q / m (in C / kg ) is of the order of

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Q. Two particles, each of mass $m$ and carrying charges $Q$, are separated by some distance. If they are in equilibrium under mutual gravitational and electrostatic forces then $Q / m$ (in $C / kg$ ) is of the order of

Electric Charges and Fields

Solution:

The attractive gravitational force $=G \frac{m^{2}}{r^{2}}$
and the repulsive electrostatic force $=k \frac{Q^{2}}{r^{2}}$.
where $r$ is the separation between two particles
For equilibrium, $\frac{G m^{2}}{r^{2}}=\frac{k Q^{2}}{r^{2}}$
or $\frac{Q}{m}=\sqrt{\frac{G}{k}}$
$=\left[\frac{6.67 \times 10^{-11}}{9 \times 10^{9}}\right]^{1 / 2} \sim 10^{-10}$