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Two identical small charged spheres are a certain distance apart, and each initially experiences an electrostatic force of magnitude F due to the other. With time, charge gradually diminishes on both spheres. When each of the spheres has lost half its initial charge, the magnitude of the electrostatic force will be

a) 1/16 F
b) 1/8 F
c) 1/2 F
d) 1/4 F

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Answer:

d) 1/4 F

Explanation:

The magnitude of electrostatic force between stationary charges is described by Coulomb's law. This law states that this force is proportional to the magnitudes of the charges:

[tex]F\propto q_1q_2[/tex]

When each of the spheres has lost half its initial charge, we have:

[tex]q_1'=\frac{q_1}{2}\\q_2'=\frac{q_2}{2}[/tex]

So, the new electrostatic force is:

[tex]F'\propto q_1'q_2'\\F'\propto \frac{q_1}{2}\frac{q_2}{2}\\F'\propto \frac{q_1q_2}{4}\\F'\propto\frac{1}{4}F[/tex]

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