Answer:
The magnitude of charge on each is [tex]5.707\times 10^{13} C[/tex]
Solution:
As per the question:
Mass of Earth, [tex]M_{E} = 5.98\times 10^{24} kg[/tex]
Mass of Moon, [tex]M_{M} = 7.35\times 10^{22} kg[/tex]
Now,
The gravitational force of attraction between the earth and the moon, if 'd' be the separation distance between them is:
[tex]F_{G} = \frac{GM_{E}M_{M}}{d^{2}}[/tex] (1)
Now,
If an identical charge 'Q' be placed on each, then the Electro static repulsive force is given by:
[tex]F_{E} = \frac{1}{4\pi\epsilon_{o}}\frac{Q^{2}}{d^{2}}[/tex] (2)
Now, when the net gravitational force is zero, the both the gravitational force and electro static force mut be equal:
Equating eqn (1) and (2):
[tex]\frac{GM_{E}M_{M}}{d^{2}} = \frac{1}{4\pi\epsilon_{o}}\frac{Q^{2}}{d^{2}}[/tex]
[tex](6.67\times 10^{- 11})\times (5.98\times 10^{24})\times (7.35\times 10^{22}) = (9\times 10^{9}){Q^{2}}[/tex]
[tex]\sqrt{\farc{(6.67\times 10^{- 11})\times (5.98\times 10^{24})\times (7.35\times 10^{22})}{9\times 10^{9}}} = Q[/tex]
Q = [tex]\pm 5.707\times 10^{13} C[/tex]
