Question

Two identical particles each of mass $M$ and charge $Q$ are placed a certain distance part. If they are in equilibrium under mutual gravitational and electric force then calculate the order of $\frac{Q}{M}$ in $SI$ units.

Answer 1

As the given system of charges are in equilibrium,

hence $F_e=F_g$

$F_e$ is the electric force between the charges which is

repelling them while $F_g$ is the gravitational force of attraction.

ie. $\frac{K{Q}^2}{R^2}=\frac{G{M}^2}{R^2}$

or , $K{Q}^2=G{M}^2$

or , $(\frac{Q}{M}{)}^2=(\frac{G}{K})$

or , $\frac{Q}{M}=(GK{)}^{\frac{1}{2}}$

as G = $6.67\times {10}^{-11}N{m}^2/K{g}^2$

and K = $9\times {10}^{9}N{m}^2/C^2$

$(\frac{Q}{M}{)}^2=\frac{(6.67\times {10}^{-11})}{(9\times {10}^9)}$

or $\frac{Q}{M}=[0.7411\times {10}^{-(11+9)}{]}^{\frac{1}{2}}$

or $\frac{Q}{M}=(0.7411\times {10}^{-20}{)}^{\frac{1}{2}}$

we get $\frac{Q}{M}=0.86\times {10}^{-10}$ c / kg