(26 points) Suppose Earth and the Moon each carried a net negative charge -Q. In

Question

(26 points) Suppose Earth and the Moon each carried a net negative charge -Q. Instead
of using two flat spheres, approximate both bodies as point masses and point charges.

(a) (8 points) Find an equation for Q when the electrical and gravitational forces balance.
(b) (8 points) What value of Q is required to balance the gravitational attraction between
Earth and the Moon?
(c) (6 points) Does the distance between Earth and the Moon affect your answer? Explain
why.
(d) (4 points) How many electrons would be needed to produce this charge?

Explanation / Answer

A.

Given that both force balances, So

Fq + Fe = 0

Fq = -Fe

|Fq| = |Fe|

given that charge on both earth and moon are same, So

k*Q*Q/r^2 = G*Me*Mm/r^2

r = distance between earth and moon

k*Q^2 = G*Me*Mm

Q = sqrt (G*Me*Mm/k)

Part B.

We know that

Me = Mass of earth

Mm = mass of moon

k = 9*10^9

G = 6.67*10^-11

Using these

Q = sqrt (6.67*10^-11*5.98*10^24*7.35*10^22/(9*10^9))

Q = 5.71*10^13 C

Part C.

Since expression

Q = sqrt (G*Me*Mm/k)

does not depends on distance between moon and earth so it will not affect our answer.

Part D.

We know that Charge is given by:

Q = n*e

n = number of electrons = ?

e = charge on single electron

So,

n = Q/e

n = 5.71*10^13/(1.6*10^-19)

n = 3.57*10^32 electrons

Please Upvote. Comment below if you have any doubt.

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