Question

The Earth and Moon are bound to-gether by gravity. If, instead, the force of attrac-tion were the result of each having a charge of thesame magnitude but opposite in sign, find the quantity of charge that would have to be placed on each to produce the required force.

Answer 1

Charge on Moon and Earth is 5.43x10¹³ C .

Step-by-step explanation:

Gravitational force is the force of attraction between any two bodies having mass while Electrostatic force is the force experienced by two charge bodies. Electrostatic force can be attractive or repulsive.

Let M and m be the mass of Earth and Moon respectively, d is the distance between Earth and Moon and q be the charge on Earth and -q be on the Moon.

Gravitational force, F₁ =
`\frac{G*{m}*{M}}{d^(2) }`

Here G is gravitational constant.

Electrostatic force, F₂ =
`\frac{k*{q}*{q}}{d^(2) }`

Here k is Coulomb constant.

According to the problem, the gravitational force between Earth and Moon is equal to the electrostatic force between them.

F₁ = F₂

`\frac{G*{m}*{M}}{d^(2) }` =
`\frac{k*{q}*{q}}{d^(2) }`

`\frac{G*{m}*{M}}{k }` =
`q^(2)`

Put 6.07x10⁻¹¹ N m²/kg² for G, 5.97x10²⁴ kg for M, 7.34x10²² kg for m and 9x10⁹ N m²/C² in the above equation.

`\frac{6.07*{10^(-11) }*{5.97}*{10^(24)*{7.34}*{10^(22) } }}{9*{10^(9) } }` = q²

q =
`\sqrt{2.95*{10^(27) }}`

q = 5.43x10¹³ C