# (e) Imagine the Moon, with 27.3% of the radius of the Earth, had a charge 27.3% as large, with the same sign. Find the electric force the Ea

Question

(e) Imagine the Moon, with 27.3% of the radius of the Earth, had a charge 27.3% as large, with the same sign. Find the electric force the Earth would then exert on the Moon.

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1 year 2021-09-01T20:58:38+00:00 2 Answers 15 views 0

1. Explanation:

Below is an attachment containing the solution.

if Q = 1c

$$F_{e} = 7.25 N$$

Explanation:

We suposse that the earth has a charge equal to Q, then the moon would have a charge equal to 0.273 Q.

The electrical force between two objects charged is described by the Coulomb’s law

$$F_{e} = \frac{kQ_{1}Q_{2} }{r^{2} }$$

Where k is the Coulomb’s constant       $$k = 8.9874×10^{9} \frac{Nm^{2} }{c^{2} }$$

r is the distance between the earth and the moon

Then the electrical force would be:

$$F_{e} = \frac{(8.9874×10^{9}Q(0.273Q) )}{338400000}$$

$$F_{e} = 7.25 Q^{2} N$$

For estimating this force we can suppose Q = 1 C and then

$$F_{e} = 7.25 N$$