Due to cosmic shower same amount of cations +q are stored in the atmosphere of the earth and the moon. If the gravitational attraction between the earth and the moon is exactly equal to the electric repulsion between them. Then find the value of charge q stored in their atmosphere.

Explanation

Let mass of the moon and the earth be `M_(m)` and `M_(e)`. respectively and distance between them be r.
The repulsive force between them `=(qxxq)/(r^(2))=(q^(2))/(r^(2))`
and gravitational attractive force=`(GM_(e)M_(m))/(r^(2))`
According to the problem,
`(q^(2))/(r^(2))=(GM_(e)M_(m))/(r^(2))` or, `q=sqrt(GM_(e)M_(m))` esu