Chapter 24, Problem 17SP

Imagine two separated tiny interacting uniformly charged spheres. What happens to the electrostatic force on each of them if the charge on one is doubled?

To determine

Thechanges in the electrostatic force between two tiny charge spheres separated by a distance if charge on one of the spheresis doubled.

Answer to Problem 17SP

Solution:

Force on both the charges will also double.

Explanation of Solution

Given data:

The charge on one sphere is doubled.

Formula used:

Write the expression for electrostatic force for any point charge by another point charge:

$F=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r^2}$

Here, $F$ is the electrostatic force, $q_1$ charge on first point charge, $q_2$ charge on other point charge, ${\epsilon }_0$ permittivity of free space, and $r$ is the separation between the point charges.

Explanation:

Consider the expression for the electrostatic force between twopoint charges:

$F=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r^2}$

Here, $F$ is the initial electrostatic force acting on the charge particles.

Now, consider the expression for the electrostatic force between twopoint charges. This time charge $q_2$ is doubled. Therefore, the new expression becomes:

$F^{\prime }=\frac{1}{4\pi {\epsilon }_0}\frac{q_1\left(2q_2\right)}{r^2}$

Here, $F^{\prime }$ is the electrostatic force when one charge is doubled.

The force $F$ is compared with force $F^{\prime }$, which concludes that the electrostatic force on both the charges is doubled.

Conclusion:

Therefore, the electrostatic force on both the charges is doubled when change on one of the sphere is doubled.