18. When 1.6 mathrm(~kg) point charge is 15 mathrm(~m) from a second point charge, the gravitational force each one experiences is 573 mathrm(~N) . What is the mass of the second charge? Given: & Work: Formula: & Answer: 8.3 times 10^-12 mathrm(~kg) b. 1.2 times 10^11 mathrm(~kg) c. 1.2 times 10^12 mathrm(~kg) d. 8.5 times 10^12 mathrm(~kg) 19. Two electrons are 20 mathrm(~m) apart at closest approach. What is the magnitude of the maximum electric force that they exert on each other? (c=-1.60 times 10^-14 mathrm(C)) Given: & Work: Formula: & Answer: a. 1.2 times 10^-9 mathrm(~N) b. 5.8 times 10^11 mathrm(~N) c. 2.5 times 10^-6 mathrm(~N) d. 1.6 times 10^-11 mathrm(~N) 20. The force of attraction that a -40.0 mathrm(C) point charge exerts on a +108 mathrm(C) point charge has magnitude 4.00 mathrm(~N) . How far apart are these two charges? Given: & Work: Formula: & Answer: a. 1.38 times 10^3 mathrm(~m) b. 1.9 times 10^4 mathrm(~m) c. 3.12 times 10^4 mathrm(~m) d. 9.71 times 10^2 mathrm(~m)

### Question 18:<br />**Given:**<br />- Mass of the first charge, \( m_1 = 1.6 \, \text{kg} \)<br />- Distance between charges, \( r = 15 \, \text{m} \)<br />- Gravitational force, \( F_g = 573 \, \text{N} \)<br /><br />**Formula:**<br />The gravitational force between two masses is given by Newton's law of gravitation:<br />\[<br />F_g = G \frac{m_1 m_2}{r^2}<br />\]<br />Where:<br />- \( G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \) (gravitational constant),<br />- \( m_1 \) and \( m_2 \) are the masses,<br />- \( r \) is the distance.<br /><br />Rearranging for \( m_2 \):<br />\[<br />m_2 = \frac{F_g \cdot r^2}{G \cdot m_1}<br />\]<br /><br />**Substitute values:**<br />\[<br />m_2 = \frac{573 \cdot (15)^2}{6.674 \times 10^{-11} \cdot 1.6}<br />\]<br /><br />\[<br />m_2 = \frac{573 \cdot 225}{1.06784 \times 10^{-10}}<br />\]<br /><br />\[<br />m_2 = \frac{128925}{1.06784 \times 10^{-10}} \approx 1.2 \times 10^{12} \, \text{kg}<br />\]<br /><br />**Answer:** \( c. 1.2 \times 10^{12} \, \text{kg} \)<br /><br />---<br /><br />### Question 19:<br />**Given:**<br />- Distance between electrons, \( r = 20 \, \text{m} \),<br />- Charge of an electron, \( q = -1.60 \times 10^{-11} \, \text{C} \).<br /><br />**Formula:**<br />The electric force between two charges is given by Coulomb's law:<br />\[<br />F_e = k \frac{|q_1 q_2|}{r^2}<br />\]<br />Where:<br />- \( k = 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \) (Coulomb constant),<br />- \( q_1 \) and \( q_2 \) are the charges,<br />- \( r \) is the distance.<br /><br />Since both charges are electrons (\( q_1 = q_2 = q \)):<br />\[<br />F_e = k \frac{q^2}{r^2}<br />\]<br /><br />**Substitute values:**<br />\[<br />F_e = 8.99 \times 10^9 \cdot \frac{(-1.60 \times 10^{-11})^2}{20^2}<br />\]<br /><br />\[<br />F_e = 8.99 \times 10^9 \cdot \frac{2.56 \times 10^{-22}}{400}<br />\]<br /><br />\[<br />F_e = 8.99 \times 10^9 \cdot 6.4 \times 10^{-25}<br />\]<br /><br />\[<br />F_e \approx 5.75 \times 10^{-15} \, \text{N}<br />\]<br /><br />**Answer:** The magnitude of the maximum electric force is approximately \( 5.75 \times 10^{-15} \, \text{N} \).<br /><br />---<br /><br />### Question 20:<br />**Given:**<br />- Charges: \( q_1 = -40.0 \, \text{C}, q_2 = +108 \, \text{C} \),<br />- Force: \( F = 4.00 \, \text{N} \).<br /><br />**Formula:**<br />Using Coulomb's law:<br />\[<br />F = k \frac{|q_1 q_2|}{r^2}<br />\]<br /><br />Rearranging for \( r \):<br />\[<br />r = \sqrt{\frac{k |q_1 q_2|}{F}}<br />\]<br /><br />**Substitute values:**<br />\[<br />r = \sqrt{\frac{8.99 \times 10^9 \cdot |(-40.0)(108)|}{4.00}}<br />\]<br /><br />\[<br />r = \sqrt{\frac{8.99 \times 10^9 \cdot 4320}{4.00}}<br />\]<br /><br />\[<br />r = \sqrt{\frac{3.88032 \times 10^{13}}{4.00}}<br />\]<br /><br />\[<br />r = \sqrt{9.7008 \times 10^{12}} \approx 9.71 \times 10^6 \, \text{m}<br />\]<br /><br />**Answer:** \( d. 9.71 \times 10^6 \, \text{m} \)