Equal charges are deposited on two spherical bodies, each having a mass of 50 kg and positioned 20 cm apart. If the magnitude of the Coulomb repulsion between them exactly balances their gravitational attraction, determine the magnitude of the charge on each body.

Step-by-step solution

The Coulomb repulsion force between the two charges is given by F_e = 1 4 ₀ q^2 r^2 The gravitational attraction force between the two masses is given by F_g = G m^2 r^2 Since the Coulomb repulsion exactly balances the gravitational attraction, we have F_e = F_g 1 4 ₀ q^2 r^2 = G m^2 r^2 q^2 = 4 ₀ G m^2 q = m 4 ₀ G Substituting the given values m = 50 kg , G = 6.67 10⁻¹¹ N m ^2/ kg ^2 , and 1 4 ₀ = 9 10^9 N m ^2/ C ^2 : q = 50 6.67 10⁻¹¹ 9 10^9 q = 50 0.741 10⁻²⁰ q 50 0.86 10⁻¹⁰ q 43 10⁻¹⁰ C = 4.3 10⁻⁹ C