Consider a system of two charges of magnitude 2times 10^-7C and 4.5times 10^-7 C which is acted upon by a force of 0.1 N. What is the distance between the two charges? 1.2 m 2 m .09 m .81 m

To find the distance between the two charges, we can use Coulomb's law, which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.<br /><br />Mathematically, Coulomb's law can be expressed as:<br /><br />\[ F = \frac{{k \cdot |q_1| \cdot |q_2|}}{{r^2}} \]<br /><br />where:<br />- \( F \) is the force between the charges (in newtons, N)<br />- \( k \) is the Coulomb constant (\( 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \))<br />- \( q_1 \) and \( q_2 \) are the magnitudes of the charges (in coulombs, C)<br />- \( r \) is the distance between the charges (in meters, m)<br /><br />Given:<br />- \( F = 0.1 \, \text{N} \)<br />- \( q_1 = 2 \times 10^{-7} \, \text{C} \)<br />- \( q_2 = 4.5 \times 10^{-7} \, \text{C} \)<br /><br />We need to find \( r \).<br /><br />Rearranging the formula to solve for \( r \):<br /><br />\[ r = \sqrt{\frac{{k \cdot |q_1| \cdot |q_2|}}{{F}}} \]<br /><br />Substituting the given values:<br /><br />\[ r = \sqrt{\frac{{(8.99 \times 10^9) \cdot (2 \times 10^{-7}) \cdot (4.5 \times 10^{-7})}}{{0.1}}} \]<br /><br />\[ r = \sqrt{\frac{{8.99 \times 10^9 \cdot 9 \times 10^{-14}}}{{0.1}}} \]<br /><br />\[ r = \sqrt{8.091 \times 10^{-4}} \]<br /><br />\[ r \approx 0.0284 \, \text{m} \]<br /><br />Therefore, the distance between the two charges is approximately 0.0284 meters, which is closest to option 3,.09 m.