Chapter 16, Problem 6P

To determine

The magnitude of the new force.

Answer to Problem 6P

The magnitude of the new force is $2.048\text{N}$ .

Explanation of Solution

Given:

Force exerted by two dust charged particle, $F=3.2\times {10}^{-2}\text{N}$

Formula used:

Let the magnitude of the first dust charged particle is $Q_1$ and the magnitude of the second dust charged particle is $Q_2$ . The distance between the charged particles is $r$ .

Write the expression to calculate the magnitude of force acting between two charges using Coulomb’s law.

  $F=k\frac{Q_1{Q}_2}{r^2}$.... (1)

Where,

The force acting between two charges is $F$ .

The Coulomb’s constant is $k$ and its value is $8.988\times {10}^9\text{N}\cdot {\text{m}}^{\text{2}}{\text{/C}}^2$ .

Calculation:

When the two charged dust particles are at a distance of one-eighth, the distance between becomes $\frac{r}{8}$ .

So, the expression to calculate the magnitude of new force acting between two charges using Coulomb’s law will be

  $\begin{array}{c}{F}_{\text{new}}=k\frac{Q_1{Q}_2}{{\left(\frac{r}{8}\right)}^2}\\ =64k\frac{Q_1{Q}_2}{{\left(r\right)}^2}\\ =64F\end{array}$.... (2)

Substitute the values in equation (2).

  $\begin{array}{c}{F}_{\text{new}}=64\times 3.2\times {10}^{-2}\text{N}\\ =2.048\text{N}\end{array}$

Conclusion:

Therefore, the magnitude of the new force is $2.048\text{N}$ .