Question

Suppose a charge +q on Earth’s surface and another +q charge is placed on the surface of the Moon,

1. Calculate the value of q required to balance the gravitational attraction between Earth and Moon
2. Suppose the distance between the Moon and Earth is halved, would the charge q change?
   (Take m_E = 5.9 x 10²⁴ kg, m_M = 7.348 x 10²² kg)

Answer 1

Mass of the Earth, M_E = 5.9 x 10²⁴ kg

Mass of the Moon, M_M = 7.348 x 10²² 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/(4pi epsilon_0) "q"^2/"r"^2 = ("GM"_"E" xx "M"_"M")/"r"^2`

q² = G × M_E × M_M × 4πε₀ = 320.97 × 10²⁵

q = `sqrt(320.97 xx 10^25)`= 5.665 x 10¹³ = 5.67 x 10¹³ C

(b) The distance between Moon and Earth is

`1/(4pi epsilon_0) "q"^2/("r"/2) = ("GM"_"E" xx "M"_"M")/("r"/2)`

so q = 5.67 x 10¹³ C

There is no change.