Chapter 23, Problem 104A

To determine

The distance between two charges for a given force between them.

Answer to Problem 104A

The distance of separation of the two charges is $0.4\text{ m}$.

Explanation of Solution

Given:

Two charges of $2.0\times {10}^{-5}\text{ C}$ and $8.0\times {10}^{-6}\text{ C}$ experience a force between them is 9.0 N

Formula used:

According to Coulomb’s law, two charges $q_1$ and $q_2$ separated by a distance r will experience a force between them which is equal to

  $F=K\times \frac{q_1{q}_2}{r^2}$ …… (1)

Where,

K is the proportionality constant also known as Coulomb’s constant

Calculation:

The value of Coulomb’s constant is $K=9.0\times {10}^9\text{ N}{\text{.m}}^2/{\text{C}}^2$ . Now, by substituting the charges and the force between them in (1) , the distance can be calculated as,

  $\begin{array}{c}{r}^2=K\times \frac{q_1{q}_2}{F}\\ =9.0\times {10}^9\times \frac{2.0\times {10}^{-5}\times 8.0\times {10}^{-6}}{9}\\ =0.16{\text{ m}}^2\\ r=\sqrt{0.16}\\ =0.4\text{ m}\end{array}$

Conclusion:

Therefore, the distance of separation between the charges for a given force is 0.4 m.