Suppose that the attraction between the moon and the earth were due to Coulomb forces rather than gravitational force. What would be the magnitude of the charge required if equal but opposite charges resided on both earth and moon? Mass of earth = 5.98×1024 kg; mass of moon = 7.35×1022 kg; earth-moon distance = 3.84×108 m.
I have been trying to use Fe/Fg = k/G q^2/m^2 to try to find the ratio but I'm not sure exactly what to do
G*M1*M2 would have to equal k Q^2
Q = sqrt (G M1 M2/k)
Solve that
To find the magnitude of the charge required if the attraction between the Earth and the Moon were due to Coulomb forces instead of gravitational force, you can follow these steps:
Step 1: Identify the relevant formulas:
Based on Coulomb's Law, the force between two charged objects is given by: Fe = k * q1 * q2 / r^2
Where:
- Fe is the electrostatic force between the two objects
- k is the Coulomb's constant (8.99 x 10^9 N m^2/C^2)
- q1 and q2 are the magnitudes of the charges on the two objects
- r is the distance between the centers of the two objects
Step 2: Understand the problem:
In this scenario, we have an equal but opposite charge residing on both the Earth and the Moon. By setting the gravitational force equal to the electrostatic force, we can determine the magnitude of the charge required.
Step 3: Calculate the gravitational force (Fg):
The gravitational force between two objects is given by: Fg = G * (m1 * m2) / r^2
Where:
- Fg is the gravitational force between the two objects
- G is the gravitational constant (6.674 x 10^-11 N m^2/kg^2)
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two objects
Plugging in the given values:
- mass of Earth (m1) = 5.98 x 10^24 kg
- mass of Moon (m2) = 7.35 x 10^22 kg
- distance between Earth and Moon (r) = 3.84 x 10^8 m
Fg = G * (m1 * m2) / r^2
Fg = (6.674 x 10^-11 N m^2/kg^2) * (5.98 x 10^24 kg * 7.35 x 10^22 kg) / (3.84 x 10^8 m)^2
Step 4: Calculate electrostatic force (Fe):
By setting Fg = Fe, we can find the magnitude of the charge (q) required.
Fe = Fg
k * q1 * q2 / r^2 = (6.674 x 10^-11 N m^2/kg^2) * (5.98 x 10^24 kg * 7.35 x 10^22 kg) / (3.84 x 10^8 m)^2
Substituting -q for q1 or q2 (since the charges are equal but opposite in sign):
k * q^2 / r^2 = (6.674 x 10^-11 N m^2/kg^2) * (5.98 x 10^24 kg * 7.35 x 10^22 kg) / (3.84 x 10^8 m)^2
Step 5: Solve for q:
To find the magnitude of the charge (q), rearrange the formula to isolate q:
q^2 = [(6.674 x