Suppose a charge + q on Earth's surface and another +q charge is placed on the surface of the Moon . (a) Calculate the value of q required to balance the gravitational attraction between Earth and Moon (b) Suppose the distance between the Moon and Earth is halved would the charge q change ? (Take `m_(E)= 5.9xx10^(24)kg m_(M)= 7.348 xx10^(22) kg)`

Explanation

Mass of the Earth `M_(E) = 5.9xx10^(24)` kg
Mass of the moon `M_(M) = 7.348 xx10^(22)` kg
Charge placed on the surface of Earth and Moon = q
(a) Required charge to balance the `F_(G)` between Earth and Moon
`F_(C)= F_(G) "(or)" (1)/(4piepsilon_(0)) (q^(2))/(r^(2)) = (GM_(E)xxM_(M))/(r^(2))`
`q^(2)= GxxM_(E)xxM_(M)xx4piepsilon_(0)= 320 .97 xx10^(25)`
`q= sqrt(320.97xx10^(25)) = 5.665 xx10^(13)=5.67xx10^(13)C`
(b) The distance between Moon and Earth is
`(1)/(4piepsilon_(0))(q^(2))/(r) = (GM_(E)xxM_(M))/(r) `
So q `= 5.67 xx10^(13)C`
There is no change .