Question

If the Earth had a charge of -q and the moon had a charge of +q, then find the amount of charge on each celestial body in order to create the required force.

a) -q on Earth, +q on the Moon
b) +q on Earth, -q on the Moon
c) -2q on Earth, +2q on the Moon
d) It's impossible

Answer 1

To balance the gravitational pull between the Earth and the Moon with electrostatic repulsion, each must hold an equal but opposite charge of 5.1x10^13 C.

Step-by-step explanation:

The question is asking us to determine the charge necessary on both the Earth and the Moon for their electrostatic repulsion to counteract the gravitational attraction between them. This involves equating the gravitational force to the electrostatic force and solving for the charge.

Given that the gravitational force (Fgravity) is attractive and the electrostatic force (Felectrostatic) is repulsive for charges of opposite signs, the force magnitudes must be equal for them to counteract each other, namely:

Fgravity = Felectrostatic

Using Newton's law of universal gravitation and Coulomb's law, we can write:

(G * MassEarth * MassMoon) / distance2 = (k * q2) / distance2

Simplifying and solving for 'q' will yield the necessary charge. From the provided options, the correct charge necessary on both Earth and the Moon would be option a) 5.1x1013 C, which would provide the correct balance between gravitational pull and electrostatic repulsion.