Two insulating small spheres are rubbed together and then positioned 1 cm apart. If they attract one another with a force of 0.1 N , determine the approximate number of electrons transferred from one sphere to the other during the rubbing process.

Step-by-step solution

When two spheres are rubbed together, they acquire equal and opposite charges. Let the number of electrons transferred be n . The magnitude of charge on each sphere is q = ne . Using Coulomb's law, the force of attraction is given by: F = 1 4 ₀ q^2 r^2 Substituting the given values F = 0.1 N and r = 1 cm = 10⁻² m : 0.1 = 9 10^9 q^2 (10⁻²)^2 0.1 = 9 10^9 q^2 10⁻⁴ q^2 = 0.1 10⁻⁴ 9 10^9 = 10⁻⁵ 9 10^9 = 1 9 10⁻¹⁴ q = 1 3 10⁻⁷ C Since q = ne , the number of electrons transferred is: n = q e = 1 3 10⁻⁷ 1.6 10⁻¹⁹ n = 10⁻⁷