Chapter 20, Problem 10STP

To determine

To Choose: The correct option.

Answer to Problem 10STP

B. $5.0\times {10}^{-9}\text{N}$

Explanation of Solution

Given:

The charge on the balloon, $q_1=-8.9\times {10}^{-14}\text{C}$

The charge on the metal sphere, $q_2=25\text{C}$

The distance between balloon and metal sphere, $r=2\text{}\text{km = 2000 m}$

Formula used:

The electrostatic force between two charges, $q_1$ and $q_2$ , $r$ distance apart is given by,

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

Where ${\epsilon }_0=\text{ permittivity of free space}=8.85\times {10}^{-12}\text{F/m}$

Calculation:

Using the given values in above formula, the magnitude of the force between balloon and sphere will be,

  $\begin{array}{c}F=\frac{1}{4\pi \left(8.85\times {10}^{-12}\right)}\frac{\left(8.9\times {10}^{-14}\right)\left(25\right)}{{\left(2000\right)}^2}\\ =5.0\times {10}^{-9}\text{N}\end{array}$

Conclusion:

Hence, the magnitude of the force between balloon and sphere is $5.0\times {10}^{-9}\text{N}$ .