a +32.2 μc charge feels a 0.544 n force from a +12.3 μc charge. how far apart are they? (μ stands for…

Explanation:

Step1: Convert units

Convert micro - coulombs to coulombs. $q_1 = 32.2\times10^{- 6}\text{ C}$, $q_2=12.3\times10^{-6}\text{ C}$

Step2: Use Coulomb's law formula

Coulomb's law is $F = k\frac{\vert q_1q_2\vert}{r^{2}}$, where $k = 9\times10^{9}\text{ N}\cdot\text{m}^{2}/\text{C}^{2}$. We need to solve for $r$. Rearranging the formula for $r$ gives $r=\sqrt{k\frac{\vert q_1q_2\vert}{F}}$. Substitute the values: [ \begin{align*} r&=\sqrt{9\times 10^{9}\times\frac{32.2\times10^{-6}\times12.3\times10^{-6}}{0.544}}\ &=\sqrt{9\times 10^{9}\times\frac{396.06\times10^{-12}}{0.544}}\ &=\sqrt{9\times 10^{9}\times7.28\times10^{-10}}\ &=\sqrt{6.552}\ \end{align*} ]

Answer:

$2.56\text{ m}$