Question
Asked Jan 25, 2019
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How much equal charge should be placed on the Earth and the Moon so that the electrical repulsion balances the gravitational force of 1.98×10^20N? Treat the Earth and Moon as point charges a distance 3.84×10^8m apart.

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Expert Answer

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Step 1

Find how much equal charge should be placed on the Earth and the Moon to balance the electrical repulsive force with the gravitational force.

Given information:

The gravitational force between earth and moon is equal to the electrostatic repulsive force act between charges placed on them.

The magnitude of the gravitational force is 1.98 x1020 N.

Distance between Earth and Moon is 3.84 x108 m.

Equal charges are placed on the Earth and Moon.

Step 2

Formula used:

We apply Coulomb’s law to find the magnitude of charges.

This law states that the electrostatic force acts between two charges in proportional to the product of the charges and inversely proportional to the square of the distance between them.

Here, k is the coulombic   constant, q1 and q2 are two-point charges and r is the distance between charges.

Using equation-1 electrostatic force acts between Earth and the moon is,

Here, qE is the charge on earth, qM is the charge on moon. rEM is the distance between Earth and Moon.

As charge on the Earth and the Moon is same.

Rearrange the equation to find the product of charges.

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Step 3

Calculation:

Substitute all the given values in equation-...

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