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

Question

Quizplus · Accepted Answer

The electrostatic force between two charged spheres is given by Coulomb's law:
$$F=k\frac{q^2}{r^2}$$

Where $k$ is Coulomb's constant, $q$ is the charge on each sphere, and $r$ is the distance between the spheres.

Since the spheres are identical, they initially have the same charge $q_0$ and therefore the magnitude of the electrostatic force between them is given by: 
$$F=k\frac{q_0^2}{r^2}$$

When each sphere has lost half its initial charge, its charge becomes $q_0/2$. At this point, the distance between the spheres remains the same, so the magnitude of the electrostatic force between them becomes:

$$F'=k\frac{(q_0/2)^2}{r^2}= \frac{1}{4} F$$

Therefore, the magnitude of the electrostatic force on each sphere is $\boxed{	extbf{(C)}\ 1/4\ F}$.

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